-~7 


LOGIC 


INDUCTIVE  AND  DEDUCTIVE 


AN    INTRODUCTION    TO  SCIENTIFIC    METHOD 


BY 
ADAM  LEROY 


ADJUNCT  PROFESSOR  OF  PHILOSOPHY 
IN   COLUMBIA   UNIVERSITY 


NEW  YORK 
HENRY  HOLT  AND  COMPANY 


,'„•*.*  .COPYRIGHT,    1909, 

BY 
HENRY  HOLT  AND  COMPANY 


UNIV 


To 

L.  S.  M. 


574274 


PREFACE 

THIS  book  is  intended  as  a  text-book  and  not  at  all 
as  a  contribution  to  logical  theory.  It  aims  to  present 
{in  outline  of  scientific  method  as  briefly  and  as  con- 
cretely as  possible.  It  is  not  designed  to  serve  as  an 
introduction  to  general  philosophy.  Its  chief  claim  to 
novelty  is  in  the  arrangement  of  the  subject  matter. 
The  traditional  arrangement  in  which  the  deductive 
processes  are  presented  first  usually  leaves  with  the 
student  the  impression  that  method  is  chiefly  deduction, 
and  that  there  is  no  very  close  connection  between  this 
and  the  rest  of  subject.  The  arrangement,  which  is 
here  adopted,  was  selected  on  pedagogical  grounds  and 
not  in  the  interests  of  any  epistemological  theory. 

The  justification  for  dogmatic  statements  on  dis- 
puted points  is  also  pedagogical.  Argument  on  such 
points  in  a  text-book  usually  fails  to  interest  the  stu- 
dent and  often  tends  to  make  him  think  that  the  whole 
subject  is  in  an  uncertain  state  and  mostly  a  matter  of 
opinion.  Some  subjects  are  treated  much  more  briefly 
than  they  deserve,  but  I  wished  to  keep  them  in  due 
proportion  with  the  rest. 

Fallacies  are  first  discussed  along  with  the  processes 
with  which  they  are  connected,  but  they  are  all  brought 
together  in  a  later  chapter.  Many  of  the  exercises  are 
new,  but  I  have  also  drawn  freely  from  other  text- 
books. The  longer  exercises  at  the  end  of  the  book 
give  the  student  an  opportunity  to  bring  to  bear  al- 


vi  PREFACE 

most  the  whole  of  scientific  method,  and  for  this  reason 
they  seem  to  me  to  be  very  important. 

My  indebtedness  to  Jevons,  Hyslop,  Mill,  and  Bow- 
ley  will  be  obvious.  I  owe  much  to  Aikins'  Principles 
of  Logic;  his  broader  treatment  of  many  topics  and 
his  chapters  on  Testimony,  Averages,  Statistics,  etc., 
were  very  suggestive.  Sidgwick's  The  Use  of  Words 
in  Reasoning,  Creighton's  treatment  of  the  Figures 
of  the  Syllogism  in  his  Introduction  to  Logic,  Hibben's 
use  of  the  idea  of  system  in  his  Logic  and  Cramer's 
The  Method  of  Darwin,  were  also  suggestive.  I  have 
tried  to  give  credit  in  each  case  in  which  I  am  con- 
scious of  having  borrowed. 

I  am  much  indebted  to  three  of  my  former  col- 
leagues in  Princeton  University:  to  Professor  W.  T. 
Marvin  for  going  over  the  whole  of  the  copy  and  giv- 
ing me  much  useful  advice,  and  to  Professors  W.  H. 
Sheldon  and  E.  M.  Rankin  for  assistance  with  the 
proof;  and  to  my  colleagues,  Professors  Woodbridge 
and  Montague,  for  many  valuable  discussions  of 
logical  problems. 

A.  L.  J. 

NEW  YORK,  April,  1909. 


CONTENTS 

PART   I 
AN   OUTLINE    OF  SCIENTIFIC   METHOD 

CHAPTER    I 
INTRODUCTORY 

PAGE 

Science  and  Common  Sense — Induction  and  Deduction  in- 
cluded in  Scientific  Method— The  Beginning  of  knowl- 
edge— Natural  Sciences  and  others — The  Sources  of 
Knowledge,  Direct  and  Indirect — Organizing  knowledge 
— Classification  as  a  preliminary  step — Language  as  a 
necessary  instrument — Further  steps  in  organized  knowl- 
edge— What  is  presupposed? 1 

CHAPTER    II 
FIRST   STAGES    IN    KNOWLEDGE 

Facts  and  "the  ways  in  which  they  are  known — Perception 
and  what  it  includes — Indirect  means  to  knowledge  of 
facts*  ......... 13 

CHAPTER   III 
CLASSIFICATION 

Types  of  Classification — Division — Requirements  of  Classi- 
fication .  .  .  .  .  . .  .  o  32 

CHAPTER   IV 

THE    USE    AND    MISUSE    OF   WORDS 
Discrimination,  Conception,  Abstraction — Necessity  for  Lan- 
guage—Terms— Kinds     of     Terms— Definition— Defects 

of  Definitions 45 

vii 


viii  CONTENTS 

PAGS 
CHAPTER    V 

PROPOSITIONS 

Kinds  of  Propositions — Propositions  and  Terms — The  Rela- 
tion of  Subject  and  Predicate — The  Distribution  of 
Terms  in  a  proposition — Euler's  Method — Ambiguous 
Propositions 66 

CHAPTER    VI 
INDUCTION 

Generalization  and  what  it  includes — Causal  Connection — 
Testing  Inductive  inferences — Complete  Enumeration — 
How  Generalizations  are  verified — Observation  and  An- 
alysis are  pre-supposed — Postponing  inference  till  test 
conditions  are  present — The  Inductive  Methods.  .  .  79 

CHAPTER   VII 

VERIFICATION    AND    DEDUCTION 
Verification    and    Deduction — Systematic    Knowledge — How 
propositions    are    related    to    each    other — Relations    of 
Opposition  among  propositions  which  have  not  identical 
terms — Conversion — Obversion — Contraposition      .     .     .     110 

CHAPTER    VIII 
THE    SYLLOGISM 

The  Principles  of  Syllogistic  Reasoning— The  First  Figure 
and  its  Principles — The  Second  Figure — The  Third 
Figure— The  Fourth  Figure 126 

CHAPTER    IX 
TRADITIONAL   TREATMENT   OF    THE 

SYLLOGISM 

Traditional  treatment — Moods — Figures — Note  on  the  Re- 
duction of  the  Moods  and  Figures 137 

CHAPTER    X 

ABBREVIATED    AND    COMPLEX   FORMS    OF    REASON' 
ING— HYPOTHETICAL   AND   DISJUNCTIVE 

SYLLOGISMS 

The  Enthymeme — Prosyllogism  and  Episyllogism — The  So- 
rites— Hypothetical  Reasoning — Disjunctive  Reasoning 
— More  Complex  Forms — Extra-syllogistic  Reasoning  .  15J 


CONTENTS  ix 

CHAPTER    XI  PAGE 

I.  PROOF  AND  DISPROOF  II.  FAILURE  TO  PROVE 
Various  Kinds  of  Proof — Failures  to  Prove — Fallacies  .  ,  166 
GENERAL  EXERCISES  »*..  171 

PART    II 
SUPPLEMENTARY  METHODS 

CHAPTER    I 
STATISTICS 
Statistics,  their  uses  and  limits — Correlation — The  Processes 

used   in   Statistical    Investigations 189 

CHAPTER    II 
AVERAGES 

The  Arithmetical  Average — The  "Weighted"  Average— The 
Mode — The  Median — The  Geometrical  Average — Meas- 
uring Deviations  from  an  average — Measurement  of  phe- 
nomena— The  Comparison  of  quantities  which  cannot  be 
measured  198 

CHAPTER   III 
PROBABILITY 

The  Meaning  of  Probability — Deducing  the  probability  of  a 
phenomenon — Dangers  to  be  avoided  in  interpreting 
probability 213 

SUPPLEMENT  TO    PART    II 

The  Graphic  Method  of  Representing  Data  and  Their  Re- 
lations   226 

PART    III 
THE    CONSTRUCTION    OF    SYSTEMS 

CHAPTER    I 

EXPLANATION 

What  is  Explanation?     ,     ,     , 231 


x  CONTENTS 

PAGH 
CHAPTER    II 

HYPOTHESIS 

What  is  an  Hypothesis?— The  Value  of  Hypotheses— How 
are  Hypotheses  suggested  to  us? — Requisites  of  a  good 
hypothesis 246 

CHAPTER    III 

TYPICAL  SYSTEMS   OF   KNOWLEDGE 
The  Geometric  System — Others  closely  related  to  this — Sys- 
tems which  are  more  concerned  with  concrete  phenom- 
ena— Systems    of    Historical    Facts 257 

EXERCISES   IN   THE   EXAMINATION   OF  COMPLEX   REASONING 
Professor  James's  Argument  for  his  Theory  of  the  Emotions 
— A.  H.  Fison  on  "The  Evolution  of  Double  Stars"— 
Huxley  on  "  The  Demonstrative  Evidence  of  Evolution  "    279 


PART   I 
AN    OUTLINE    OF    SCIENTIFIC    METHOD 


CHAPTER    I 
INTRODUCTORY 

Science  and  Common  Sense. — The  methods  of  sci- 1 
ence  are  the  methods  of  all  correct  thinking.  In  all 
thinking  we  are  concerned  with  getting  and  organiz- 
ing knowledge,  or  with  testing,  applying,  and  devel- 
oping the  knowledge  we  have  already  acquired.  We 
are  all  aware  that  correct  thinking  differs  from  that 
which  is  incorrect  in  its  conformity  to  certain  laws. 
These  laws  are  usually  spoken  of  as  the  laws  of 
thought.  They  are  not  simply  laws  of  thought,  how- 
ever ;  they  are  laws  of  things  as  well ;  they  are  the 
laws  of  the  world  as  we  know  it.  They  are  adhered 
to,  consciously  or  unconsciously,  in  all  correct  think- 
ing, whether  casual  or  systematic.  Science  differs  from 
common  sense  "  only  as  a  veteran  differs  from  a  raw 
recruit;  and  its  methods  differ  from  those  of  common 
sense  only  so  far  as  the  guardsman's  cut  and  thrust 
differ  from  the  manner  in  which  the  savage  wields  his 
club.  The  primary  power  is  the  same  in  each  case, 
and  perhaps  the  untutored  savage  has  the  more  brawny 
arm  of  the  two.  The  real  advantage  lies  in  the  point 
and  polish  of  the  guardsman's  weapon ;  in  the  trained 
eye,  quick  to  spy  out  the  weakness  of  the  adversary; 
in  the  ready  hand,  prompt  to  follow  it  upon  the  in- 
stant. But,  after  all,  the  sword  exercise  is  only  the 
hewing  and  poking  of  the  clubman  developed  and 
perfected. 


2  INTRODUCTORY 

"  So  the  vast  results  obtained  by  science  are  won 
.  .  .  by  no  mental  processes  other  than  those  which 
are  practised  in  every  one  of  the  humblest  and  meanest 
affairs  of  life.  A  detective  policeman  discovers  a  bur- 
glar from  the  marks  made  by  his  shoe,  by  a  mental 
process  identical  with  that  by  which  Cuvier  restored 
the  extinct  animals  of  Montmartre  from  the  fragments 
of  their  bones.  Nor  does  the  process  of  induction  and 
deduction  by  which  a  lady,  finding  a  stain  of  a  peculiar 
color  upon  her  dress,  concludes  that  somebody  has  up- 
set the  inkstand  thereon,  differ  in  any  way,  in  kind, 
from  that  by  which  Adams  and  Leverrier  discovered  a 
new  planet.  The  man  of  science,  in  fact,  simply  uses 
with  scrupulous  exactness  the  methods  which  we  all 
habitually  and  at  every  moment  use  'Carelessly ;  and 
the  man  of  business  must  as  much  avail  himself  of  the 
scientific  method — must  be  as  truly  a  man  of  science — 
as  the  veriest  bookworm  of  us  all."  1  ^ 

It  is  of  course  true  that  the  conclusions  of  science 
are  often  in  disagreement  with  those  of  common  sense, 
but  the  disagreement  is  due  to  the  difference  in  the 
thoroughness  and  completeness  with  which  the  facts 
have  been  examined.  In  many  cases  the  -common  sense 
of  to-day  is  simply  the  science  of  yesterday,  for  com- 
mon sense  is  usually  very  conservative,  and  often  re- 
gards the  novelty  of  a  conclusion  as  an  argument 
against  it. 

Induction  and  Deduction  included  in  Scientific 
Method. — Scientific  method  being  simply  a  more  thor- 
ough application  of  principles  universally  employed  in 

i  Huxley,  The  Educational  Value  of  the  Natural  History 
Sciences.  ' 


INDUCTION    AND    DEDUCTION  3 

reasoning,  a  good  means  of  getting  a  general  view  of 
those  principles  will  be  to  examine  the  procedure  of 
science.  It  includes  both  formal  and  inductive  logic. 
Formal  or  deductive  logic  is  simply  one  part  of  scien- 
tific method ;  hence  any  exposition  of  scientific  method 
will  include  an  examination  of  deduction.  Sometimes 
induction  is  identified  with  scientific  method,  but  it  is 
often  used  in  a  narrower  sense ;  and,  in  any  case,  it 
might  seem  to  exclude  deduction,  which  is  an  essen- 
tial part  of  complete  scientific  method :  therefore  it 
is  less  confusing  to  think  of  induction  as  simply  a  part 
of  scientific  method.  Inductive  and  deductive  reason- 
ing are  constituent  elements  in  a  single  system.  For 
purposes  of  study,  it  will  be  advisable  to  break  up  the 
system  into  several  parts.  The  first  of  these  parts  will 
include  the  processes  and  principles  involved  in  acquir- 
ing a  knowledge  of  facts ;  the  second,  those  employed 
in  the  classification  of  facts ;  the  third,  includes  the 
discovery  and  formulation  of  laws ;  and  the  fourth, 
the  testing  of  these  laws  and  their  further  organiza- 
tion and  application.  Each  of  these  processes  will  be 
found  to  involve  a  number  of  subsidiary  processes.  As 
they  are  parts  of  a  system,  they  are,  of  course,  mutu- 
ally dependent;  each  leads  up  to  or  implies  the 
others. 

The  Beginning  of  Knowledge. — Nowadays  there  is 
almost  universal  agreement  to  the  statement  that  all 
knowledge  begins  in  the  perception  of  concrete  facts. 
It  has  sometimes  been  thought  that  the  mind  began 
its  -career  with  a  capital  stock  of  knowledge  in  the 
form  of  "  innate "  ideas  or  principles.  But  no  one 
now  maintains  tlmt  there  is  any  knowledge  before  ex- 


4  INTRODUCTORY 

perience  begins.  That,  however,  is  no  warrant  for 
the  conclusion  which  John  Locke  drew.2  He  held  that 
the  mind,  at  the  beginning  of  its  history,  is  like  a  sheet 
of  white  paper  or  a  waxen  tablet  or  an  empty  cabinet, 
and  that  experience,  like  some  external  force,  writes 
upon  the  tablet  or  fills  the  cabinet.  To  him  the  mind 
seemed  to  be  passive  in  the  acquisition  of  knowledge, 
able  at  most  to  combine  and  analyze  its  sensations  and 
ideas.  Immanuel  Kant,  on  the  other  hand,  contended  3 
that,  even  in  those  mental  operations  in  which  the  mind 
is  seemingly  least  active,  it  is  contributing  essential 
(elements;  that  it  makes  knowledge,  as  it  were,  out  of 
.the  material  which  is  furnished  from  without ;  it  cannot 
roperate  without  material,  hence  there  is  no  knowledge 
[before  sense-experience  begins ;  but  this  sense-experi- 
ence itself  is,  in  his  view,  a  product  of  the  mind's  activ- 
ity. We  cannot  pursue  this  question  any  further;  our 
concern  is  not  with  the  philosophical  problem  of  the 
ultimate  source  of  knowledge ;  it  is  enough  for  our 
purposes  to  know  that  knowledge  begins  in  concrete 
experience,  in  perception,  in  knowing  sounds  and 
colors,  odors,  moving  objects,  pains,  pleasures,  emo- 
tions, and  so  on. 

Natural  Sciences  and  Others. — Things  and  events 
and  relations  in  the  external  world  constitute  the  data 
of  what  are  sometimes  known  as  the  "  natural  "  sci- 
ences, such  as  biology,  physics  and  chemistry.  Mental 
facts'  and  their  relations  make  up  the  data  of  psychol- 
ogy ;  they  are  quite  as  concrete  in  their  way  as  any 
physical  facts,  and  the  methods  employed  by  psychol- 

2  In  his  Essay  on  the  Human  Understanding. 
s  In  his  Critique  of  the  Pure  Reason. 


THE    SOURCES    OF    KNOWLEDGE          5 

ogists  are  the  same  as  those  used  in  the  physical 
sciences. 

Such  sciences  illustrate  almost  all  the  processes  env 
ployed  in  the  acquisition  of  knowledge,  whereas  a  sci- 
ence like  mathematics  makes  most  use  of  a  few  of  them, 
which  it  applies  and  elaborates  with  great  thorough- 
ness. We  shall  attempt  to  follow,  as  closely  as  may  be, 
the  stages  in  building  up  knowledge  as  they  appear  in 
the  natural  sciences.  As  in  knowledge  generally,  these 
sciences  begin  with  the  perception  of  facts,  external  or 
internal.  Then  sooner  or  later  they  proceed  to  classify 
arid  organize  the  knowledge  thus  gained. 

The  Sources  of  Knowledge,  Direct  and  Indirect. — 
Perception  of  concrete  facts  comes  first  as  a  source 
of  knowledge,  or  rather  as  the  primitive  form  of 
knowledge.  Its  limitations  are  obvious ;  it  is  often  far 
from  clear ;  it  is  frequently  mistaken ;  it  embraces  com- 
paratively few  facts  at  any  one  time,  and  it  does  not 
extend  beyond  the  present,  or,  at  most,  the  immediate 
past.  If  we  had  to  depend  upon  it  alone,  we  could 
never  get  together  a  body  of  knowledge.  It  is  possi- 
ble dimly  to  picture  a  mind  which  could  be  aware  only 
of  what  was  immediately  present  in  time  and  space; 
its  knowledge  would  be  rudimentary,  and  without 
knowledge  of  something  besides  the  present,  the  pres- 
ent itself  would  be  meaningless.  In  all  but  the  lowest 
types  of  consciousness  there  is  a  constant  use  of  indi~ 
red  means  to  knowledge.  Memory  is  the  first  of  these.4 
Memory  restores  a  larger  or  smaller  part  of  the 

4  It  might  perhaps  be  said  that  memory  is  direct  knowledge  of 
the  past,  and  this  is  true  in  a  sense ;  but  the  dependence  of  memory 
jupon  previous  perception,  the  fact  that  we  do  not  remember  what' 
we  have  not  previously  perceived,  shows  that  it  is  also  indirect. 


6  INTRODUCTORY 

knowledge  previously  gained  in  perception,  and  thus 
makes  it  possible  to  draw  upon  past  as  well  as  present 
experience. 

Another  indirect  means  to  knowledge  is  the  testimony 
of  others ;  by  this  means  we  can  come  into  possession 
of  a  knowledge  of  facts  which  have  never  come  under 
our  own  observation.  Oral  reports  and  written  rec- 
ords furnish  incomparably  more  information  than  any 
man's  unaided  observation  could  afford. 

A  further  way  of  extending  our  knowledge  is  to  be 
found  in  inference.  From  knowledge  which  we  already 
possess  we  are  able  to  arrive  at  conclusions  which  shall 
be  true  of  things  which  may  never  have  been  observed 
by  any  one;  we  infer  the  cause  of  a  distant  sound,  or 
the  character  of  the  other  side  of  the  moon,  or  the 
stature  and  habits  of  man's  remote  ancestors,  or  the 
climate  of  the  Northern  Hemisphere  in  the  Carbonifer- 
ous Age,  etc.  As  we  shall  see  later,  inference  is  in- 
volved in  greater  or  less  degree  in  all  the  other  means 
to  knowledge. 

An  inference  may,  of  course,  be  wrong;  if  it  is  to 
possess  any  degree  of  certainty,  there  must  be  a  con- 
siderable body  of  information  about  the  facts  in  ques- 
tion or  about  other  facts  closely  related  to  them.  The 
same  is  true,  to  a  great  extent,  of  memory,  and  even 
of  perception,  and  to  a  very  great  extent  in  the  case 
of  testimony.  Errors  may  arise  at  any  point,  and 
one  of  the  most  important  problems  in  all  thinking  is 
the  detection  and  elimination  of  errors. 

Organizing  Knowledge. — Classification  as  a  Pre- 
liminary Step. — So  far,  attention  has  been  fixed  upon 
the  processes  employed  in  acquiring  knowledge  of  facts. 


LANGUAGE  7 

In  order  to  make  this  knowledge  available,  the  data 
thus  acquired  must  be  arranged  or  classified.  The  ob- 
ject of  science  is  to  get  organized  knowledge,  and 
before  knowledge  can  be  organized  it  must  be  so  ar- 
ranged as  to  enable  us  to  see  what  facts  are  similar 
and  what  are  different.  Classification  is  the  grouping 
of  phenomena  according  to  their  likenesses  and  differ- 
ences ;  those  possessing  a  given  characteristic  are  put 
into  a  group  or  class ;  those  lacking  it  may  be  put  into 
one  or  more  other  classes.  Classes  may  be  grouped 
together  in  a  larger  class  or  subdivided  into  smaller 
ones. 

Language  as  a  Necessary  Instrument. — There  is  one 
very  important  instrument  for  the  acquisition  of 
knowledge  which  has  not  yet  been  mentioned ;  and  that 
is  language.  Without  some  means  of  describing  or 
otherwise  representing  facts,  only  a  very  limited  use 
could  be  made  of  our  perceptions:  testimony  would  be 
impossible  without  it;  inference  involves  representing 
to  ourselves  the  consequences  of  certain  principles  or 
facts  or  situations;  imagination  and  memory  are  ways 
of  representing  what  is  absent  by  means  of  pictures  of 
the  facts  themselves  or  by  means  of  other  symbols.  A 
great  variety  of  symbols  might  be  employed,  but  lan- 
guage, spoken  and  written,  supplies  by  far  the  most 
important  and  complete  set  of  symbols.  The  descrip- 
tion and  classification  of  facts  would  be  practically 
impossible  without  language. 

Further  Steps  in  Organized  Knowledge. —  In  some 
sciences:  we  find  little  more  than  classified  knowledge; 
the  so-called  "  classificatory  sciences,"  such  as  botany 
and  zoology,  have,  until  recently,  consisted  almost 


8  INTRODUCTORY 

wholly  of  classified  data.  Science  aims  not  simply  at 
classified  knowledge,  but  at  organized  knowledge,  at 
knowledge  organized  into  a  coherent  system.5  It  aims 
at  the  discovery  of  the  laws  manifested  by  its  data  as 
well  as  at  the  discovery  of  the  data  themselves  and 
their  arrangement  into  groups. 

What  is  a  scientific  law?  A  law  in  the  -field  of  sci- 
ence is  a  statement  of  the  way  in  which  things  do 
invariably  behave.  Unlike  a  moral  law,  a  scientific 
law  has  nothing  to  say  about  the  way  in  which  things 
ought  to  behave,  and,  unlike  a  civil  law,  it  does  not 
prescribe  a  mode  of  action  whose  violation  involves  a 
penalty.  The  law  of  gravitation,  for  example,  simply 
states  that  bodies  do  attract  each  other  in  certain  defi- 
nite ways ;  if  bodies  should  fail  to  do  this,  the  law  of 
gravitation  would  be  no  genuine  law.  A  scientific  law 
states  an  invariable,  unconditional  -connection  between 
phenomena. 

How  are  laws  of  this  character  discovered?  They 
are  based  originally  upon  observation  of  particular 
instances  of  the  behavior  of  phenomena.  From  ob- 
served instances  we  draw  an  inference  which  covers  all 
other  cases  of  the  sort,  past  and  future.  This,  that 
and  the  other  acid  turns  blue  litmus  paper  red ;  we 
conclude  that  all  acids  will  have  a  like  effect.  This 
conclusion  may,  of  course,  be  mistaken ;  it  is  an  infer- 
ence, and  must  be  tested  or  verified. 

Verification  is  then  the  next  step.  It  may  be  under- 
taken in  several  ways:  our  conclusion  may  be  com- 

5  There  are  of  course  fields  of  science  where  classified  knowledge 
is  the  most  that  can  be  had,  But  the  ideal  of  science  goes  beyond 
this. 


PRESUPPOSITIONS  d 

pared  with  other  things  which  we  know  about  the  facts 
under  investigation ;  it  may  be  shown  to  be  a  conse- 
quence of  some  known  law ;  or  it  may  be  possible  to 
find  some  further  fact  which  would  be  consistent  with 
our  inference  and  with  no  alternative  inference  that 
can  be  suggested.  Speaking  generally,  verification  in- 
volves finding  whether  the  inference  in  question  fits  in 
with  the  system  of  things  to  which  it  belongs.  If  such 
a  test  cannot  be  applied,  if  there  is  no  such  system  of 
which  it  can  be  shown  to  be  a  member,  it  remains 
uncertain. 

What  is  Presupposed? — One  important  question  re- 
mains to  be  asked.  Are  there  any  laws  or  universal 
propositions  which  do  not  require  verification?  Are 
there  any  statements  which  are  self-evident  and  not 
open  to  question  or  to  proof?  Axioms,  such  as  those 
of  mathematics,  are  sometimes  said  to  be  of  this  char- 
acter. For  example,  take  the  statement  that  two 
things  equal  to  the  same  thing  are  equal  to  each  other; 
can  this  statement  be  doubted  or  can  a  proof  for  it 
be  conceived?  Are  there  not  propositions  which  are 
so  fundamental  that  they  cannot  be  based  upon  any 
which  are  more  general,  and  so  necessary  to  all  thought 
that  they  cannot  be  based  upon  perception,  but  are 
presupposed  in  perception?  This  raises  again  the 
question  at  issue  between  Locke  and  Kant;  without 
attempting  to  answer  it,  we  may  at  least  say  that 
no  proposition  which  does  not  justify  itself  in  experi- 
ence can  be  accepted  as  true.  Many  propositions  have 
seemed  to  be  self-evident  only  to  be  proved  false  by 
later  development  in  knowledge,  and  whatever  else  may 
be  urged  in  favor  of  any  proposition,  it  must  at  any 


10  INTRODUCTORY 

rate  fit  in  with  the  rest  of  the  things  we  know  if  it 
is  to  be  accepted  as  true. 

Certain  of  these  axioms  or  postulates  are  to  be  found 
in  every  science.  In  logic  they  appear  under  the  name 
of  the  Laws  of  Thought.  They  are: 

The  Law  of  Identity,  expressed  by  the  formula:  A 
is  A. 

The  Law  of  Contradiction,  expressed  by  the  formula : 
A  is  not  non-A. 

The  Law  of  Excluded  Middle:  Either  A  is  B  or  A 
is  not  B. 

The  Law  of  Sufficient  Reason:  Every  thing  which 
exists  has  a  sufficient  reason  or  cause  for  being  what 
it  is. 

There  is  some  disagreement  regarding  the  meaning 
of  some  of  these  laws.  The  Law  of  Identity,  for  ex- 
ample, seems  to  be  a  mere  tautology:  to  state  that 
A  is  A,  or  that  a  thing  is  what  it  is,  does  not  seem  to 
give  us  any  information.  It  is  true,  of  course,  that 
in  a  world  where  the  Law  of  Identity,  in  this  sense, 
did  not  hold,  reason  could  do  nothing.  But  the  Law 
of  Identity  is  usually  taken  to  mean  also  that  there 
must  be  an  element  of  identity  in  every  act  of  thought 
and  in  every  piece  of  reasoning.  In  the  proposition 
"  Man  is  rational,"  it  is  obvious  that  man  and  rational 
are  not  identical;  still  there  is  something  common  to 
the  two;  without  this  core  of  identity  no  single  judg- 
ment would  be  possible. 

The  Law  of  Contradiction  complements  the  Law  of 
Identity.  A  thing  is  not  its  opposite,  and  in  so  far 
as  there  is  opposition  between  two  things  it  is  neces- 
sary to  assert  that  one  is  not  the  other. 


THE    LAWS    OF    THOUGHT  11 

The  Law  of  Excluded  Middle  asserts  that  of  two 
contradictory  statements  one  or  the  other  must  be 
true.  The  law  does  not  hold  if  the  two  statements  are 
not  contradictory,  i.e.,  if  there  is  any  third  possibility. 
There  is  a  middle  ground  between  "  A  is  brilliant  "  and 
"  A  is  stupid  " :  he  may  be  an  average  person.  But 
"  This  figure  is  square "  and  "  This  figure  is  not 
square  "  are  contradictories. 

All  these  laws  are,  of  course,  laws  for  thought,  but 
they  are  equally  laws  of  things,  and  they  are  laws 
for  thought  for  that  reason  only.  Certainly  they 
must  hold  for  any  world  in  which  reason  can  operate. 

The  Law  of  Sufficient  Reason  asserts  that  the  uni- 
verse is  a  rational  universe;  that  for  everything  that 
exists  there  is  a  reason,  and  an  adequate  reason;  that 
things  are  capable  of  explanation,  implying  that  the 
world  is  a  coherent  system.  In  the  words  of  Leibniz, 
who  gave  the  principle  its  rank,  ".  .  .  nothing 
occurs  for  which  one  having  sufficient  knowledge  might 
not  be  able  to  give  a  sufficient  reason  why  it  is  as  it  is 
and  not  otherwise." 6  If  the  world  were  entirely 
chaotic,  knowledge,  except  that  of  the  most  primitive 
sort,  would  be  impossible ;  there  could  be  no  general 
knowledge,  no  knowledge  of  laws  or  principles,  for  laws 
and  principles  would  not  exist.  It  is  conceivable,  how- 
ever, that  the  world  is  only  partly  rational,  that  there 
are  things  for  which  there  is  no  sufficient  reason ;  if  so, 
rational  knowledge  would  be  limited  to  the  fields  within 
which  principles  did  hold. 

Summarizing,  we  may  say  that  every  science  aims 

6  Principes  de  la  Nature  et  de  la  Grace.  Quoted  in  Dictionary 
of  Philosophy,  Ed.  J.  Mark  Baldwin,  Art.  "Sufficient  Reason." 


12  INTRODUCTORY 

at  the  discovery  of  the  laws  of  the  data  with  which 
it  deals,  and  at  the  organization  of  all  its  content  into 
a  single  systematic  whole.  A  completely  organized 
system  of  knowledge  would  be  one  in  which  every  part 
would  imply  every  other,  and  he  who  understood  the 
system  perfectly  could  reconstruct  the  whole  from  any 
part.  Cuvier  claimed  that  a  naturalist  could  recon- 
struct an  animal  from  a  single  bone,  and  he  himself, 
as  noted  by  Huxley  in  the  passage  quoted  above,  gave 
evidence  of  the  validity  of  his  claim.  Perfection  of 
organization  is  not  to  be  found  in  any  natural  science; 
the  mathematical  sciences  show  something  approxi- 
.mating  completeness,  but  they  do  not  deal  directly  with 
concrete  facts. 


CHAPTER    II 
FIRST    STAGES    IN    KNOWLEDGE 

I.  Facts  and  the  Ways  in  Which  They  are  Known. — 
Knowledge  begins  with  the  perception  of  facts;  and 
these  facts  are  of  many  kinds.  What  is  a  fact? 
A  fact  is  anything  which  exists ;  it  is  that  which 
is  real,  apart  from  any  opinion  we  may  have  about  it 
or  any  attitude  which  we  may  take  toward  it ;  it  is 
that  which  is  as  opposed  to  that  which  is  merely  imag- 
ined or  conceived.  When  we  ask  for  facts,  we  ask  for 
something  which  shall  be  independent  of  any  belief  1  or 
disbelief,  approval  or  disapproval,  on  the  part  of  any 
person.2  Some  or  all  of  these  characteristics  belong  to 
laws,  but  fact  is  distinguished  from  law  in  being  con- 
crete and  particular,  instead  of  abstract  and  general. 

A.  PERCEPTION  AND  WHAT  IT  INCLUDES. — Facts 
are  known  primarily  through  perception  and  memory ; 
they  are  known  directly  only  by  means  of  perception, 

1  Belief   and   disbelief,   whether   true   or   false,   are   themselves 
facts;  they  are  psychological  facts.     Belief  in  the  Ptolemaic  as- 
tronomy was  a  fact;  that  is,  the  belief  actually  existed.    A  false 
belief  is  one  in  which  the  thing  believed  is  not  a  fact;  it  asserts 
or  assents  to  something  which  does  not  really  exist.    Belief  or  dis- 
belief may  bring  about  changes  in  facts;  in  other  words,  give  rise 
to  new  facts,  as  may  any  other  existing  thing.     To  say  that  a  fact 
is  independent  of  our  attitude  means  that  its  existence  and  char- 
acter are  what  they  are  apart  from  our  attitude  and  aside  from 
any  possible  effects  which  may  be  produced  upon  them  by  our 
attitude. 

2  This    position    is    confessedly    dogmatic.      Further    reflection 
uiight  show  that  nothing  is  independent,  but  for  our  present  pur- 
pose this  position  is  justified. 

13 


14        FIRST    STAGES    IN    KNOWLEDGE 

though  there  are  various  ways  in  which  they  may  be 
known  indirectly.  One  of  the  most  important  of  these 
indirect  means,  and  one  which  is  an  important  element 
in  all  the  rest,  is  inference;  a  perceived  fact  may  be 
evidence  to  our  minds  of  the  existence  of  something 
which  we  cannot  perceive. 

Much  that  is  often  included  under  perception  must 
be  eliminated  when  we  are  trying  to  use  the  term  with 
scientific  accuracy.  For  example,  we  say  that  we  per- 
ceive the  inkstand  upon  the  table,  or  a  man  on  the 
other  side  of  the  street,  or  that  lightning  has  set  fire 
to  a  distant  building,  or  that  Mr.  X  is  an  able  law- 
yer, or  that  history  repeats  itself,  and  so  on.  Are  any 
of  these  pure  perceptions?  We  may  perceive  certain 
events,  but  to  "  perceive  "  that  history  is  therein  re- 
peating itself  involves,  at  the  very  least,  these  infer- 
ences :  that  the  words  of  historians  represent  what  has 
occurred  in  the  past;  that  they  are  competent  and 
truthful  and  that  we  understand  them;  and  that  the 
events  we  perceive  are  really  like  those  which  they  have 
described.  In  the  example  of  the  lawyer,  we  base  our 
belief  on  observation  of  certain  acts  of  his  which  have 
brought  about  desired  results  in  spite  of  difficulties ; 
and  on  the  inferences  that  he  understood  the  situation 
and  intended  to  bring  about  the  results  which  actually 
occurred.  Again,  though  the  flash  and  the  distant 
light  were  perceived,  the  conclusions  that  the  flash  was 
lightning  and  that  the  light  was  that  of  a  burning 
building  in  the  distance,  and  that  the  first  of  these  was 
the  cause  of  the  second,  involve  far  more  than  percep- 
tion. In  such  instances  as  these  the  presence  of  infer- 
ence is  evident  and  the  importance  of  distinguishing 


PERCEPTION    AND    INFERENCE          15 

what  is  perceived  from  what  is  inferred  is  obvious. 
The  perception  might  be  correct,  while  the  inference 
was  erroneous,  or  vice  versa.  By  distinguishing  the 
two,  the  problems  of  discovering  error  and  of  correct- 
ing it  are  much  simplified. 

But  it  is  by  no  means  easy  to  know  where  to  draw 
the  line  between  perception  and  inference.  We  should 
say  ordinarily  that  we  perceive  the  ink-well  or  the  man 
across  the  street,  but  even  in  these  cases  there  is  some- 
thing which  is  very  like  inference.  A  perception  con- 
tains many  different  elements,  and  these  get  themselves 
before  the  mind  in  a  variety  of  ways ;  comparatively 
little  in  any  perception  can  be  said  to  come  directly 
from  the  object.  In  the  perception  of  the  ink-well  or 
the  man  all  that  we  get  directly  is  a  spot  of  color 
with  certain  variations  of  light,  shade,  and  so  on.  But 
we  seem  to  see  an  object  in  three  dimensions,  of  a  cer- 
tain size,  at  a  given  distance  from  us,  and  possessing 
weight,  resistance,  a  certain  degree  of  hardness,  a  pe- 
culiar internal  structure  and  an  indefinite  number  of 
other  qualities,  which  may  be  more  or  less  definitely 
present  to  the  mind.  If  we  had  not,  in  the  past,  found 
these  qualities  in  combination  with  spots  of  color  sim- 
ilar to  those  now  present,  we  should  not  be  aware  of 
them  now;  but  that  does  not  mean  that  these  qualities 
are  simply  remembered,  for  they  are  present  to  the 
mind  as  genuinely  objective  qualities,  and  we  seem  to 
be  as  directly  aware  of  them  as  we  are  of  the  color, 
although  reflection  shows  us  that  they  could  not  be 
given  by  sight  alone.  They  all  seem  to  present  them- 
selves together,  while  in  remembering  a  number  of 
events,  first  one  appears  before  the  mind  and  then  an- 


16        FIRST   STAGES    IN    KNOWLEDGE 

other;  in  perceiving  an  object,  the  qualities  do  not  come 
forward  one  after  another,  but  all  seem  to  be  present 
together  in  a  single  thing.  A  perception  is  a  reaction 
of  the  mind  to  an  object,  quality,  or  event  of  some  kind. 
!A  mind  which  has  had  little  experience  in  a  given  field 
will  react  to  an  object  in  that  field  with  a  perception 
of  a  comparatively  simple  sort;  if  one  had  seen  and 
handled  oranges  but  had  not  tasted  them,  his  percep- 
tion would  contain  no  suggestion  of  the  flavor,  as  a 
blind  man's  perception  contains  no  suggestion  of  color 
or  other  visual  qualities. 

Every  time  an  object  is  perceived  under  new  condi- 
tions something  is  added  which  will  modify  future  per- 
ceptions in  greater  or  less  degree.  The  child  builds  up 
his  perceptions  gradually ;  from  a  first  vague,  indefi- 
nite perception  he  advances  to  one  that  is  more  coher- 
ent and  complete. 

The  way  in  which  any  person  will  perceive  an  object 
will  depend  largely  upon  his  past  experience:  different 
persons  will  consequently  perceive  the  same  object  dif- 
ferently; as  no  two  persons  have  ever  had  precisely 
the  same  experience,  they  will  never  see  a  given  object 
in  precisely  the  same  way.  But  in  most  instances  the 
differences  will  be  slight,  because  there  is  so  much  that 
is  common  in  the  experience  of  all,  and  in  the  percep- 
tion of  ordinary  objects  the  differences  are  usually 
small  and  comparatively  unimportant. 

"  Fallacies  "  of  Perception,  and  Their  Causes. — We 
think  of  perception  as  a  certain  and  infallible  source 
of  knowledge ;  but  if  in  all  perceptions  there  is  a  large 
addition  from  past  experience  it  is  clear  that  many 
of  them  are  likely  to  be  wrong.  The  present  object  may 


CAUSES    OF    MISTAKEN    PERCEPTIONS      17 

not  be  similar  in  all  respects  to  like  objects  which  we 
have  seen  in  the  past.  A  spot  of  color  of  a  certain 
shape  and  apparent  size  may  have  stood  invariably 
for  an  orange ;  in  other  words,  it  may  have  been  found 
along  with  other  sensations  indicating  a  solid  spherical 
object,  of  a  certain  flavor  and  odor,  with  a  certain  in- 
ternal structure,  and  so  on.  If  the  spot  of  color  again 
appears  we  seem  to  be  aware  of  the  other  qualities. 
But  there  may  be  only  a  spot  of  color,  as  on  the 
painter's  canvas.  Again,  when  two  persons  are  similar 
in  appearance,  one  may  easily  be  mistaken  for  the 
other.  The  visual  appearance  of  A  may  seem  to  as- 
sure the  presence  of  the  other  qualities  which,  as  a 
matter  of  fact,  belong  to  B. 

The  possibility  of  erroneous  perceptions  was  com- 
mented upon  very  early  in  the  history  of  thought,  and 
because  errors  of  this  sort  occur  so  frequently,  some 
thinkers  concluded  that  the  senses  were  altogether  unre- 
liable as  sources  of  knowledge.  Others  urged  that  the 
fault  was  not  with  the  senses;  they  pointed  out  that 
the  trouble  lay  in  adding  to  what  the  senses  gave. 
When  we  have  a  sensation  of  greenness,  they  said, 
greenness  is  actually  present  to  the  mind ;  if  we  go  on 
to  say  that  there  is  present  an  apple,  we  are  adding  a 

.  number  of  qualities  to  those  which  are  given  by  sensa- 
tion, and  the  qualities  we  add  may  not  really  be  there. 

:  If  we  should  refrain  from  adding  those  other  qualities 
we  should  never  be  mistaken,  but  it  is  impossible  en- 

.  tirely  to  separate  the  sensational  element  from  the 
others.  The  perception  is  a  unit  in  spite  of  the  com- 
plexity of  the  qualities  which  make  it  up,  and  these 
qualities  are  capable  of  modifying  each  other.  The 


18        FIRST    STAGES    IN    KNOWLEDGE 

green  of  a  picture  or  of  a  landscape  does  not  look  the 
same  if  the  scene  is  looked  at  upside  down;  of  course 
we  should  be  correct  in  saying  that  we  seem  to  see  a 
certain  shade  of  green  in  the  first  case  and  a  different 
one  in  the  second.  We  may  be  perfectly  certain  with 
regard  to  what  we  seem  to  see ;  but  then  we  seem  to  see 
an  object  as  having  three  dimensions,  when  it  may  have 
only  two,  as  in  a  painting;  what  we  usually  want  to 
know  is  whether  we  see  the  thing  as  it  is,  whether  other 
people  seem  to  see  the  same  thing,  whether  we  may 
expect  to  seem  to  see  it  in  the  future,  whether  handling 
the  object  would  give  confirmatory  sensations,  and  so 
on.  The  attempt  to  limit  our  statements  to  what  is 
unmistakably  before  the  mind  takes  us  a  very  little 
way  toward  -certainty  in  knowledge.  Perceptions  in- 
clude more  than  that.  They  should,  of  course,  be  made 
as  carefully  as  possible.  But  although  errors  are  cer- 
tain to  occur,  yet  if  we  do  not  run  this  risk  of  error  we 
make  little  progress  toward  knowledge. 

This  first  form  then  in  which  knowledge  appears  is 
open  to  mistake ;  there  are  mistaken  perceptions.  It 
may  be  well  to  note  the  different  types  of  error  and 
their  chief  causes.  The  types  are  usually  said  to  be 
two;  and  they  have  been  called  Mai-observation  and 
Non-observation.  The  names  are  self-explanatory. 
Mai-observation  is  of  two  kinds :  in  the  one,  something 
which  does  not  belong  to  the  object  is  added  in  the 
perception ;  in  the  other,  the  relations  of  the  parts  are 
wrongly  perceived,  as  when  we  read  there  for  three. 
Of  course,  both  kinds  of  mal-observation  may  be  pres- 
ent together,  and  non-observation  also.  Otherwise 
stated,  there  are  really  three  kinds  of  error;  omission, 


THREE    KINDS    OF    ERROR  19 

addition  and  wrong  relation  of  the  parts  in  a  whole. 
They  may  occur  at  any  stage  in  knowledge,  and  they 
are,  in  fact,  the  only  kinds  which  can  occur  at  any 
stage.  What  are  their  causes  in  the  field  of  percep- 
tion? A  passage  from  Bacon,  quoted  by  Jevons,  calls 
attention  to  a  number  of  the  causes  which  give  rise  to 
them:  "Things  escape  the  senses  because  the  object 
is  not  sufficient  in  quantity  to  strike  the  sense:  as  all 
minute  bodies;  because  the  percussion  of  the  object  is 
too  great  to  be  endured  by  the  senses:  as  the  form  of 
the  sun  when  looking  directly  at  it  in  mid-day ;  be- 
cause the  time  is  not  proportionate  to  actuate  the 
sense:  as  the  motion  of  a  bullet  in  the  air,  or  the  quick 
circular  motion  of  a  fire-brand,  which  are  too  fast,  or 
the  hour  hand  of  a  common  clock,  which  is  too  slow; 
from  the  distance  of  the  object  as  to  place:  as  the  size 
of  celestial  bodies,  and  the  size  and  nature  of  all  dis- 
tant bodies;  from  prepossession  by  another  object:  as 
one  powerful  smell  renders  other  smells  in  the  same 
room  imperceptible;  from  the  interruption  of  interpos- 
ing bodies :  as  the  internal  parts  of  animals ;  and  be- 
cause the  object  is  unfit  to  make  an  impression  upon 
the  sense:  as  the  air,  or  the  invisible  and  untangible 
spirit  which  is  included  in  every  living  body." 

The  various  kinds  of  causes  may  be  classified  as 
follows : 

1.  In  the  first  place,  the  external  or  physical  con- 
ditio-ns  of  the  perception  may  be  unfavorable ;  in  a  red 
or  green  light,  the  color  of  objects  is  wrongly  seen; 
in  a  fog,  sounding  objects  seem  nearer  than  they  really 
are;  if  the  light  is  dim,  details  are  overlooked;  if  we 
look  through  an  imperfect  window-pane,  objects  ap- 


20        FIRST    STAGES    IN    KNOWLEDGE 

pear  distorted.  In  all  these  cases  there  is  something  in 
the  medium  through  which  the  object  is  perceivec] 
which  leads  to  error.  Similar  difficulties  arise  when 
instruments  are  employed  to  extend  the  range  or  in- 
crease the  accuracy  of  our  perceptions.  Any  imper- 
fection in  the  instrument  is  almost  certain  to  be  a  fruit- 
ful source  of  error.  Other  things  might  be  cited  in 
this  field,  but  these  will  suffice  to  illustrate  the  class. 

2.  Next  in  order  we  may  mention  the  physiological 
causes  of  mistaken  perceptions.     Imperfections  in  the 
sense-organ,  fatigue,  illness,  and  the  like  are  obvious 
examples.     There  is   one  sort   of  perception   which  is 
always  inaccurate,  that  of  the  time  at  which  an  event 
occurs ;   a  flash  of  lightning  is   seen  a  fraction   of  a 
second  after  the  light  reaches  our  eyes ;  a  sound  is  not 
heard  in  the  instant  at  which  it  reaches  our  ears.     The 
reason  is  this :  a  thing  cannot  be  perceived  until  the 
nerve  current  which  it  sets  up  in  our  sense-organ  has 
passed   along   through   the  nerves   to   the  brain ;   this 
takes  time,   and  in  some  -cases,   as  in   astronomy,   the 
errors  which  arise  from  this   source  may  be  very  im- 
portant.    Again,  we  often  tend  to  perceive  an  event 
for  a  moment   after  it  has   ceased,   since  the  nervous 
system  continues  to  reverberate,  as  it  were,  after  the 
original  cause  of  its  activity  has  ceased  to  act.     Hence 
the  flash   or   sound  seems   to  be  present  after  it  has 
really  passed.     This  is  seen  in  our  inability  to  distin- 
guish the  spokes  of  a  rapidly  revolving  wheel  or  the 
successive  vibrations  of  a  tone,  or  single  views  in  mov- 
ing pictures ;  in  all  these  the  succeeding  event  begins 
before  we  have  ceased  to  perceive  the  one  before  it. 

3.  But  if  all  physiological  and  physical  conditions 


PSYCHOLOGICAL  CAUSES  OF  ERROR  21 

were  favorable,  if  all  organs  and  media  and  instru- 
ments were  perfect,  there  would  still  remain  the  psycho- 
logical sources  of  error.  These  are  often  or  even 
always  present  along  with  the  others.  One  of  the  psy- 
chological causes  has  already  been  alluded  to,  namely, 
(1)  the  tendency  to  see  what  we  have  previously  seen 
in  similar  circumstances.  There  is  also  (2)  a  tendency 
to  perceive  what  we  expect  or  wish  or  hope  or  fear,  or 
what  has  been  recently  or  habitually  in  the  mind,  or 
that  which  has  been  vividly  perceived  or  imagined. 
What  is  known  as  the  "  proof-reader's  "  illusion  illus- 
trates one  of  these;  in  reading,  the  context  often  sug- 
gests a  certain  word  and  we  see  that  word  and 
overlook  mistakes  in  spelling.  In  the  following  passage 
(based  on  one  in  James's  Psychology)  few  persons 
reading  at  the  ordinary  rate,  and  with  ordinary  care, 
would  succeed  in  detecting  all  the  mistakes  in  spelling : 
Any  one  wateing  in  a  dark  plase  and  expectng  or  faer- 
ing  a  certaon  objectt  will  interpret  an  abrup  seusation 
to  mean  that  object's  presense.  The  boy  playing  "  I 
spy,"  the  criminel  skulhing  from  his  persuers,  the 
superstitions  personn  hureying  throuh  the  churchvard 
at  midnight,  the  man  losst  in  the  woods,  the  girl  who 
tremulusly  has  made  an  eveniug  apointmnt  with  her 
swain,  all  are  subjec  to  ilusions  of  sight  and  sound 
wkich  make  there  hearts  beat  til  they  ate  dispelld. 

Another  case  illustrating  some  of  these  principles  is 
that  of  the  prisoner  who  had  already  been  convicted 
of  one  crime  and  served  his  sentence,  and  who  narrowly 
escaped  conviction  a  second  time,  although  entirely 
innocent  in  both  cases.  He  bore  a  superficial  resem- 
blance to  the  real  criminal;  the  witnesses  were  predis- 


22        FIRST    STAGES    IN    KNOWLEDGE 

posed  to  believe  that  he  was  the  criminal,  and  they 
positively  identified  him  as  the  one  whom  they  had  seen 
committing  the  crime. 

The  effectiveness  of  all  these  tendencies  is  enhanced 
by  (3)  lack  of  attention  or  misplaced  attention.  The 
inattentive  reader  overlooks  misprints,  and  so  does  the 
reader  who  is  very  intent  upon  the  thought.  Presti- 
digitators, fraudulent  spiritualistic  mediums,  and  the 
like,  take  advantage  of  these  tendencies.  They  direct 
attention  to  unimportant  things  in  order  that  they 
may  do  the  important  ones  unobserved,  and  by  leading 
the  spectator  to  expect  certain  events  they  can  often 
persuade  him  to  believe  that  he  actually  witnesses  them. 

Mistakes  as  to  the  order  of  events  are  very  easy  in 
some  circumstances;  if  two  events,  one  in  the  field  of 
sight  and  the  other  in  that  of  sound,  occur  very  nearly 
at  the  same  time,  this  often  happens.  (4)  Lack  of 
training  in  observing  events  of  a  given  kind  may  make 
correct  perception  impossible;  the  use  of  the  micro- 
scope, finding  and  following  a  trail  in  the  woods^ 
seeing  distant  objects  at  sea  or  on  the  plains,  distin- 
guishing flavors,  colors,  etc.,  are  examples. 

(5)  Abnormal  psychological  conditions,  such  aa, 
nervous  excitement,  those  produced  by  drugs,  etc., 
modify  the  keenness  and  accuracy  of  perceptions, 
sometimes  for  the  better  and  sometimes  for  the  worse. 
These  various  causes,  physical,  physiological  and  psy- 
chological, are  so  closely  bound  up  together  that  it  is 
often  difficult  to  say  which  is  chiefly  operative  in  any 
given  case. 

Careful  and  intelligent  attention  will  prevent  many 
errors.  A  careful  perception  made  with  a  purpose  is 


OBSERVATION  23 

called  an  observation.  This  term  is  sometimes  used  to 
cover  all  perception  whatsoever,  but  it  will  be  used 
here  in  the  narrower  sense.  Still,  the  most  carefully 
made  perception  may  prove  to  be  mistaken.  In  some 
of  the  sciences  there  are  various  special  and  technical 
methods  of  eliminating  error.3 

The  discovery  of  error  does  not  always  lead  to  its 
elimination  nor  enable  us  to  make  the  requisite  correc- 
tion. In  some  cases  it  does ;  we  have  already  seen  that 
the  perception  of  an  event  takes  time;  this  time  is 
longer  for  some  persons  than  for  others,  but  for  each 
it  is  approximately  constant  under  given  conditions. 
By  means  of  a  device  which  registers  the  exact  time  at 
which  a  certain  event  occurs  and  the  time  at  which  the 
observer  indicates  that  he  perceives  it,  it  is  possible  to 
determine  his  "  personal  error "  and  to  make  the 
proper  correction  in  cases  in  which  the  exact  time  of 
the  occurrence  cannot  be  otherwise  determined.  But 
in  most  cases  it  is  riot  possible  to  do  this  or  even  to 
guess  at  the  presence  or  the  amount  of  error.  Some- 
times, as  in  the  case  of  measurements,  it  may  be  pos- 
sible to  repeat  the  observation,  and  if  the  results 
cannot  be  made  to  agree,  we  can  sometimes  get  a  result 
approximately  correct  by  taking  an  average. 

Testing  Perceptions. — It  can  almost  be  said  that 
every  observation  should  be  held  in  suspicion  until 
tested.  The  test  would  consist  in  finding  out  whether 
it  agreed  with  other  observations  of  the  same  fact  or 
of  similar  facts  made  by  ourselves  or  others,  whether  it 
was  in  agreement  with  the  laws  of  the  field  in  which  it 
was  found,  with  the  laws  of  Nature  generally,  and  so 
s  See  Jevons,  Principles  of  Science,  chap.  xv. 


2.4        FIRST    STAGES    IN    KNOWLEDGE 

on.  We  always  proceed  upon  the  principle  that  ail 
knowledge  should  hang  together,  should  be  consistent 
and  coherent ;  that  the  world  is  a  consistent  and 
coherent  world ;  and  that  correct  perceptions  will 
agree  with  each  other  and  with  the  rest  of  our  expe- 
rience. 

When  it  is  possible  to  repeat  an  observation,  we  have 
at  once  a  starting-point  for  testing  it ;  and  when  new 
observations  can  be  made  under  more  exact  conditions, 
we  are  in  a  very  favorable  position  for  extending  our 
knowledge  of  the  facts  under  observation.  One  of  the 
chief  reasons  why  modern  astronomy,  for  example,  is 
so  far  in  advance  of  that  of  the  Greeks  is  to  be  found 
in  the  fact  that  modern  instruments  make  the  observa- 
tions of  astronomical  phenomena  so  much  more  reli- 
able. 

Experiment. — Sometimes  it  is  possible  to  reproduce 
at  will  the  phenomenon  under  observation.  This  is  the 
case,  to  a  great  degree,  in  physics  and  chemistry: 
sounds,  chemical  changes,  and  so  on,  can  be  repeated 
indefinitely.  Moreover,  the  circumstances  in  which  the 
phenomenon  occurs  may  often  be  controlled  and  varied 
more  or  less,  and  that  is  very  often  a  matter  of  great 
importance,  as  will  appear  later.  To  bring  about  an 
event  for  the  sake  of  observing  it  is  to  experiment. 
An  experiment  may  be  performed  for  various  reasons ; 
it  may  be  that  we  wish  simply  to  get  an  additional  ob- 
servation as  a  basis  for  inference  or  a  means  of  testing 
the  accuracy  of  one  which  we  have  made  already;  or 
we  may  wish  to  see  the  result  of  changing  certain  of 
the  circumstances  in  which  the  phenomenon  occurs ;  or 
of  finding  the  consequences  of  any  condi^on  whatso" 


EXPERIMENT  25 

ever.  "  Whenever  we  can,  by  our  own  agency,  influence 
the  object  we  are  investigating,  we  can  remedy  this 
want  [insufficient  observation]  by  experiment.  We 
can  institute  at  will  a  certain  group  of  conditions  C, 
and  so  compel  the  causes  which  are  really  at  work  to 
respond  with  an  effect  E,  which  would  otherwise  per- 
haps have  never  come  within  the  domain  of  our  senses. 
By  varying  at  will  the  quantity  and  composition  of 
that  C  we  can  bring  about  in  E  a  series  of  changes  in 
quantity  and  kind,  which  were  still  less  likely  to  offer 
themselves  unsolicited  to  our  observation.  Again,  we 
can  break  up  C  into  its  component  parts,  and  in  each 
experiment  allow  but  one  of  these,  or  a  definitely  as- 
signed group  of  several  of  them,  to  take  effect,  at  the 
same  time  cutting  off  the  rest  from  action.  The  con- 
stituent elements  of  the  result  E  admit  of  being  sepa- 
rated in  the  same  way,  so  that  we  learn  which  of  them 
depends  upon  which  element  of  the  compound  C.  Thus 
experiment  is  the  practical  means  by  which  we  furnish 
ourselves  with  observations  in  such  number  and  involv- 
ing such  mutual  differences  and  affinities  as  is  requisite 
in  order  to  the  elimination  of  what  is  unessential  in 
them.  .  .  .  Defined  in  this  way,  it  is  clear  that  ex- 
periment only  has  an  advantage  over  observation  in  so 
far  as  it  is  capable  of  supplementing  the  usual  defi- 
ciencies of  the  latter ;  its  function  is  to  furnish  us  with 
suitable  and  fruitful  observations  instead  of  the  un- 
suitable and  unfruitful  ones  which  offer  themselves. 
.  .  .  It  is  merely  a  way  of  preparing  and  setting  be- 
fore ourselves  phenomena  which  it  is  of  importance  that 
we  should  observe."  4  But  its  function  is  exceedingly 
*Lotze,  Logic,  Bk.  II,  chap,  vii,  260. 


26        FIRST    STAGES    IN    KNOWLEDGE 

important,  and  without  it  many  sciences  could  make  lit- 
tle progress. 

The  peculiar  advantage  of  being  able  to  control  and 
vary  the  conditions  of  an  event  to  be  observed  will  be 
evident  at  a  later  point. 

B.  INDIRECT  MEANS  TO  KNOWLEDGE  OF  FACTS. 
I.  Memory  and  its  Defects. — So  far  in  the  present 
chapter  we  have  discussed  only  the  direct  means  of 
knowing  facts.  It  appeared,  however,  that  even  in  per- 
ception there  is  much  that  is  a  revival  of  past  experi- 
ence, reinstated  by  the  memory.  Knowledge  of  the  past, 
reappearing  in  memory,  bulks  very  large  in  the  total  of 
our  knowledge.  True  memory  is  simply  the  recall  of 
past  experience  accompanied  by  awareness  of  the  fact 
that  it  was  our  experience.  If  one  experience  or  one 
object  of  experience  is  similar  to  what  is  now  before 
our  minds,  or  if  it  has  been  related  to  the  latter  in 
any  way,  it  tends  to  reappear.  That  tendency  is  often 
overcome,  otherwise  practically  everything  would  be 
remembered.  Not  only  do  many  things  drop  out  of  the 
memory,  but  many  are  also  changed  in  their  character 
or  order,  and  some  things  may  be  added.  Ordinary  for- 
getfulness  corresponds  to  non-observation.  It  is  prac- 
tically always  present  in  greater  or  less  degree,  and 
it  obviously  tends  to  increase  with  the  lapse  of  time. 
Many  things  disappear  altogether ;  sometimes  the  main 
outlines  are  remembered  and  details  forgotten;  some- 
times only  a  few  of  the  details  remain. 

Remembering  wrongly  corresponds  to  mal-observa- 
tion:  words  which  were  correctly  heard  may  be  incor- 
rectly remembered;  an  object  which  was  seen  as  red 
may  be  remembered  as  brown,  and  so  on.  Hardly  ever 


DEFECTS    OF    MEMORY  27 

do  any  two  witnesses  agree  exactly  in  their  memory  of 
events  which  could  easily  have  been  observed  with  little 
danger  of  mistake.  This  is  so  generally  recognized 
that  too  close  a  correspondence  between  the  stories  of 
two  witnesses  is  regarded  as  an  evidence  of  collusion 
and  dishonesty. 

Besides  the  modification  of  details,  the  order  of 
events  may  be  changed  in  memory  or  their  relations  may 
be  modified  in  other  ways,  and  entirely  new  elements 
may  be  introduced.  Among  the  causes  of  mistaken 
memory  the  following  may  be  noted: 

1.  A  tendency  to  remember  what  would  usually  have 
happened  in  the  circumstances. 

2.  A  tendency  to  remember  things  or  elements  which 
were  particularly   pleasant   or   unpleasant,   desired    or 
feared,  etc.,  at  the  expense  of  those  which  were  more 
neutral.     Elements  or  events  of  this  sort,  which  did  not 
occur  but  were  suggested  or  expected,  may  be  remem- 
bered as  if  they  had  occurred. 

3.  A  tendency  to  remember  things  in  a  way  which 
would  make  them  more  complete  or  logical,  or  more  in 
agreement  with  our  own  opinions  or  wishes,  or  more  in 
harmony  with  what  we  expected,  or  feared,  etc. 

4.  Events  which  have  often  been  described  in  one's 
hearing  may  seem  to  be  remembered. 

The  tests  of  memory,  like  those  of  perception,  are 
based  upon  the  principle  that  genuine  knowledge  is 
always  consistent  and  coherent,  that  the  world  of  facts 
is  throughout  harmonious. 

Where  accurate  records  are  available  the  memory, 
as  a  source  of  knowledge  of  the  past,  becomes  much 
less  important.  Accurate  records  made  at  the  time 


28        FIRST    STAGES    IN    KNOWLEDGE 

when  the  phenomena  were  perceived  are  an  essential 
part  of  all  the  concrete  sciences.  The  methods  of  re- 
cording are  many,  and  they  are  too  technical  for  pres- 
ent discussion. 

II.  Testimony. — Written  records  and  oral  reports 
make  up  a  large  part  of  what  is  known  as  evidence. 
Besides  these,  evidence  includes  historical  remains  of 
every  sort,  products  of  man's  activity,  natural  phe- 
nomena of  every  kind,  such  as  glacial  scratches,  geo- 
logical deposits,  etc.,  etc.  The  evidence  may  be  of 
something  in  the  remote  past,  of  something  not  ob- 
served in  the  present,  or  of  future  events.  The  use  of 
evidence  clearly  involves  making  inferences;  it  also  in- 
volves perception.  Some  phenomenon  is  perceived,  such 
as  an  uttered  sound  or  an  inscription  or  a  fossil,  and 
on  the  basis  of  this  perception  the  observer  draws  con- 
clusions concerning  something  which  may  never  be  per- 
ceived. 

Oral  and  written  reports,  or,  in  other  words,  testi- 
mony, furnish  a  frequent  ground  of  inference.  Testi- 
mony includes  every  statement  of  fact  made  by  any 
one.  The  opportunities  for  error  in  using  it  are  so 
numerous  that  it  is  surprising  that  correct  information 
can  ever  be  reached  by  means  of  it. 

1.  In  the  first  place,  the  person  making  the  state- 
ment was  liable  to  error  in  many  ways  when  he  observed 
the  fact  which  his  statement  purports  to  represent. 

2.  In  the  second  place,  his  memory  is  almost  cer- 
tainly inaccurate  in  one  way  or  another. 

3.  Again,  the  words  which  he  uses  may  not  correctly 
represent  to  us  what  he  has  in  mind ;  he  may  not  use 
words  accurately,  or  he  may  use  them  in  a  sense  unfa- 
miliar to  his  hearer. 


DEFECTS    OF    TESTIMONY  29 

4.  In  the  fourth  place,  he  may  not  be  truthful;  he 
may  never  have  witnessed  what  he  pretends  to  report, 
or  he  may  intentionally  misrepresent  what  he  has  wit- 
nessed. 

These  difficulties  are  present  in  both  oral  and  written 
testimony ;  in  the  latter  there  are  additional  difficulties. 
What  seems  to  be  the  witness  of  one  person  may  be 
a  garbled  account;  or  errors  may  have  been  intro- 
duced by  a  copyist  or  an  editor.  In  oral  testimony 
cross-examination  gives  a  basis  for  testing  statements 
of  the  witness.  In  written  testimony  the  substitute  for 
this  is  found  in  other  statements  by  the  same  writers 
and  by  contemporaries ;  when  these  are  not  to  be  found, 
little  credence  can  be  given  to  the  testimony. 

III.  Inference. — Inferences  from  facts  of  every  sort 
are  also  liable  to  error.  In  every  -case  the  final  test 
is  that  of  consistency  and  coherency.  The  application 
of  the  tests. very  often  involves  complicated  reasoning 
and  a  large  body  of  special  information ;  it  will  be 
discussed  incidentally  in  later  chapters;  much  of  sci- 
entific method  is  for  the  purpose  of  making  such  tests. 

EXERCISES 

1.  How  much  is  really  observed  in  seeing  a  marksman 
shoot  a  clay  pigeon?      In  hearing  an   automobile  pass,  a 
block  away?      In  seeing  a  prestidigitator  take  an  object 
from  a  pocket  in  which  it  was  not? 

2.  What  are  the  causes  of  mal-observation  and  non-ob- 
servation in  the  following  cases? 

(1)  A  straight  stick  partly  immersed  in  water  seems 

to  be  bent. 

(2)  Two    objects    looked    at   through    a   stereoscope 

seem  to  be  one,  and  they  seem  to  be  solid  in- 
stead of  flat. 

(3)  The  sun  seen  through  a  fog   sometimes  appears 

red. 


30        FIRST    STAGES    IN    KNOWLEDGE 

(4)  Mirrors  increase  the  apparent  size  of  a  room. 

(5)  Distant  objects  appear  small. 

(6)  Patients  often  seem  to  feel  pain  in  amputated 

limbs. 

(7)  A  table  seems  to  throb  if  the  fingers  are  pressed 

against  it. 

(8)  A  rearrangement  of  the  furniture  in  a  room  is 

often  unnoticed. 

(9)  We  sometimes  seem  to  feel  the  motion  of  a  boat 

after  landing. 

(10)  There  are  marked  differences  in  what  the  ordi- 

nary good  observer,  the  artist,  and  the  botanist 
see  in  a  flower. 

(11)  Silas   Marner  mistook   Effie's   hair   for  the   lost 

gold. 

(12)  Looking   at   one's   watch   and   not  knowing   the 

time  a  moment  later. 

(13)  Not  seeing  the  people  one  meets. 

(14)  In  Poe's  Sphinx,  a  small  animal  on  the  window 

pane  is  thought  to  be  a  large  moth  of  a  strange 
species. 

(15)  Mistaking  the  order  of  numbers,  as  546  for  564. 

(16)  Finding   a   likeness   between   an  infant   and   its 

parents. 

(17)  Macbeth  seeing  Birnam  Wood  coming  to  Dunsi- 

nane. 

(18)  The  pain  of  amputation  when,  instead  of  am- 

putation, an  icicle  is  drawn  across  a  limb. 

(19)  Shooting  a  man  for  a  deer  when  hunting  in  the 

woods. 

(20)  The  child's  "  seeing  "  things  at  night. 

3.  Give   five   examples   of   mistaken   observation   arising 
from  each  kind  of  cause  described  in  the  text. 

4.  Suggest  causes  for  errors  of  memory  in  the  follow- 
ing cases: 

(1)  Memory  of  "the  good  old  days  "  as  better  than 

the  present. 

(2)  Remembering  the   childhood   of   men  who   later 

became   famous. 


EXERCISES  31 

(3)  In  Ivanhoe,  Wamba  tells  the  travelers  to  go  in 

one  direction*,  but  points  in  the  other;  one  of 
them  remembers  the  verbal  directions,  the 
other  the  direction  pointed  out. 

(4)  Forgetting    cases    which    do    not    support    one's 

view. 

(5)  Forgetting  certain  items  in  lists  of  things  to  be 

bought,  etc. 

(6)  Dropping  out  characters  or  events  in  remember- 

ing a  story  or  play. 

(7)  Ascribing  to  one  person  words  or  deeds  of  an- 

other. 

(8)  "  Remembering  "   events  which  occurred  before 

one  was  born. 

(9)  "  Remembering "    the     apt    replies    which    one 

might  have  made. 

(10)  Remembering  as  an  actual  experience  what  was 
merely  a  fiction  often  related  as  an  experi- 
ence. 

5.  In  how  many  different  ways  could  you  account  for 
the  statement  of  a  witness  that  he  had  seen  a  ghost? 

6.  Suppose   three   honest   witnesses   to   have  testified  to 
seeing   a  man   catch   a   bullet  in  his  teeth:     What  would 
your  conclusion  be  ? 

7.  How  would  you  test  the  statement:     General  X  was 
killed  in  the  battle  of  Gettysburg? 


CHAPTER    III 
CLASSIFICATION 

OBJECTS  of  experience  make  their  appearance  in  an 
order  which  seems  to  be  almost  chaotic ;  and  in  memory 
they  are  often  reproduced  very  much  in  the  order  in 
which  they  originally  occurred.  But  even  in  memory, 
and  still  more  in  reflection,  there  is  a  tendency  to 
arrange  things  according  to  their  likenesses  and  differ- 
ences. This  is  the  beginning  of  classification.  Classi- 
fication "  is  not  identical  with  collection.  It  denotes 
the  systematic  association  of  kindred  facts,  the  collec- 
tion, not  of  all,  but  of  relevant  and  crucial  facts." 

A  -classification  is  necessarily  based  on  a  similarity 
of  some  sort:  of  quality  or  structure  or  origin,  and  so 
on.  Any  given  collection  of  things  may  be  classified 
in  many  different  ways.  Books,  for  example,  may  be 
grouped  according  to  subject,  size,  style  of  binding, 
publisher,  and  so  on ;  minerals,  according  to  composi- 
tion, value  or  chemical  properties ;  the  people  of  a  city, 
according  to  race,  income,  occupation  or  religion.  Any 
quality  or  relation  whatever  may  serve  as  a  basis  of 
classification.  In  the  abstract,  one  may  be  as  good  as 
another,  and  the  one  to  be  employed  in  a  given  instance 
will  be  that  which  best  serves  the  purpose  we  have  in 
hand.  There  are  several  different  types  of  classification, 
each  serving  a  special  purpose. 

Types  of  Classification.— 1.  INDEX   CLASSIFICATION.— 

1  Karl  Pearson,   The   Grammar  of  Science,  chap.   III.,  n.   1. 


CLASSIFICATION  33 

We  may  notice  briefly  the  "  Index  Classification."  2 
The  purpose  of  this  mode  of  grouping  is  to  enable  us 
to  get  hold  of  a  given  fact  quickly  and  easily.  Cata- 
logues are  usually  constructed  with  this  end  in  view, 
and  they  illustrate  the  principles  involved.  Certain 
obvious  characteristics  are  selected,  and  very  often  a 
given  item  may  appear  under  several  different  heads, 
as  in  cross-references.  Alphabetical  catalogues  are  the 
most  familiar  examples  of  the  index  classification. 

2.  DIAGNOSTIC   CLASSIFICATION. — A   second  type  is 
the   "  Diagnostic    Classification " ;   its    purpose   is   the 
identification  of  an  object  or  the  discovery  of  the  group 
to  which  it  belongs.     "  Nature  Study  "  books  abound 
in  classifications  of  this  sort.     Here,  too,  certain  obvi- 
ous characteristics  are  made  the  basis  of  classification. 
Flowers,  for  example,  may  be  classified  according  to 
color  or  time  of  appearance  or  habitat;  or  the  main 
divisions  may  be  made  upon  one  basis,  as  color,  the  first 
subdivision  on  another,  as  time  of  appearance,  etc.    The 
identification    of    ailments    by    the    physician    depends 
upon  a  classification  of  symptoms  made  upon  this  plan. 

3.  "  NATURAL  "  AND  "  ARTIFICIAL  "  CLASSIFICATIONS. 
— Both  index  and  diagnostic  classifications  are  useful, 
but  they  do  not,  by  themselves,  lead  directly  to  any 
greater  knowledge  of  the  facts  or  of  their  essential  re- 
lations.    They  are  based,  for  the  greater  part,  upon 
superficial  and  easily  noticed  characteristics,3  and  have 
little  relation  to  the  essential  properties  of  th&  things 
classified.     It  is  often  possible,  however,  so  to  group 

2  See  Jevons,  Principles  of  Science,  chap.  xxx. 

3  A  diagnostic  classification  which  is  to  be  a  sure  means  for  the 
identification  of  any  and   all  cases  should  be  based  on  essential 
qualities.    Those  based  on  superficial  and  striking  qualities  serve 


34  CLASSIFICATION 

phenomena  as  to  display  at  once  their  most  significant 
characteristics.  Compare,  for  example,  the  popular 
classification  of  the  whale  as  a  fish  with  the  scientific 
classification  of  the  same  animal  as  a  mammal.  To  call 
a  whale  a  fish  is  to  imply  that  it  lives  in  the  water,  but 
tells  little  more ;  to  call  it  a  mammal  tells  us  that  it  has 
warm  blood,  lungs  instead  of  gills,  a  four-chambered 
heart,  certain  peculiarities  of  the  skeleton,  and  so  on. 

Grouping  data  in  such  a  way  as  to  make  manifest 
at  once  their  essential  characteristics  is  the  aim  of 
classification  in  science.  Since  science  aims  at  complete 
and  systematic  knowledge,  it  will  obviously  select  as 
the  basis  of  classification  in  any  given  case  that  quality 
which  does  correlate  the  greatest  amount  of  knowledge 
about  the  facts  under  consideration. 

Scientists  usually  make  a  distinction  between  "  arti- 
ficial "  and  "  natural  "  classifications.  "  It  would  be 
possible  to  classify  all  living  things  according  to  color, 
as  white,  yellow,  green  organisms,  etc.  Such  a  classifi- 
cation would,  however,  be  artificial  and  destitute  of  sci- 
entific value  because  based  upon  a  purely  artificial  and 
highly  inconstant  character.  An  interesting  example 
of  an  artificial  classification  formerly  employed  is  the 
system  of  Linnaeus,  who  classified  flowering  plants  into 
Monandria,  Diandria,  Triandria,  Tetrandria,  etc.,  ac- 
cording to  the  number  of  stamens.  This  was  sufficiently 
convenient  for  a  first  rough  arrangement,  but  was  soon 
found  to  lead  to  the  most  incongruous  association  of 
plants  agreeing  in  the  number  of  stamens  but  differing 
in  almost  all  characters.  From  such  cases  it  is  plain 
that  plants  and  animals  cannot  be  naturally  classified 

for  ready  identification  of  many  cases,  but  not  for  all.  See  Bosar- 
quet's  Logic  for  a  discussion  of  Diagnostic  Classification  as  one 
based  upon  deeper  and  more  essential  qualities. 


NATURAL    CLASSIFICATIONS  35 

by  likenesses  or  differences  in  a  single  character  arti- 
ficially selected.  The  entire  organisms  must  be  taken 
into  account,  and  the  natural  classification  differs  from 
the  artificial  one  in  representing  real  relationship  and 
not  merely  superficial  likeness.  Modern  biology  teaches 
that  this  relationship  is  of  precisely  the  same  nature 
.as  human  relationship,  i.e.,  that  it  is  due  to  community 
of  descent  from  ancestral  plants  or  animals.  .  .  , 
'The  labor  of  determining  the  natural  classification  is 
much  lightened  by  the  fact  that  certain  structures  are 
•often  found  as  a  matter  of  experience  to  be  constantly 
.associated  or  -correlated,  so  that  the  presence  of  one 
indicates  the  presence  of  the  others.  In  such  cases  a 
single  character  may  be  taken  as  the  basis  of  a  classi- 
fication which  is  natural,  because  agreement  in  one 
character  has  been  previously  proved  empirically  to  in- 
dicate agreement  in  the  others.  For  example,  it  has 
been  proved  that  the  differences  or  resemblances  of  ani- 
mals are  correlated  with  corresponding  differences  or 
resemblances  in  their  teeth.  Hence  mammals,  to  a  great 
extent,  can  be  classified  according  to  the  structure  and 
disposition  of  the  teeth.  And  so  in  many  groups  it 
is  usually  possible  to  discover  empirically  some  one  or 
few  characters  on  which,  by  reason  of  their  constant 
association  with  other  characters,  a  natural  classifica- 
tion can  be  based."  4 

Biology  furnishes  one  of  the  best  illustrations  of  a 
field  in  which  a  natural  classification  can  be  made,  al- 
though even  here  in  many  cases  there  is  no  universal 
agreement  as  to  which  is  the  natural  classification.  For 
each  of  two  characters  or  sets  of  characters  might  be 
-correlated  with  a  number  of  others,  and  it  might  be 
4  Sedgwick  and  Wilson,  Biology,  p.  175. 


36  CLASSIFICATION 

difficult  to  decide  which  of  the  two  correlated  the 
greater  number  or  the  more  important  ones.  Even  if 
there  were  such  agreement,  it  would  not  necessarily  be 
permanent;  new  information  might  result  in  the  selec- 
tion of  a  new  basis  of  relationship.  The  difference  be- 
tween natural  and  artificial  classifications  is,  as  Jevons 
points  out,  one  of  degree  only :  "  It  will  be  found  al- 
most impossible  to  arrange  objects  according  to  any 
circumstance  without  finding  that  some  correlation  of 
other  circumstances  is  thus  made  apparent." 

The  principle  employed  in  classification  for  scientific 
purposes  is  well  stated  in  Huxley's  definition,  which  was 
modified  somewhat  by  Jevons  and  stated  in  the  follow- 
ing form :  "  By  the  classification  of  any  series  of  ob- 
jects is  meant  the  actual  or  ideal  arrangement  together 
of  those  things  which  are  like  and  the  separation  of 
those  which  are  unlike,  the  purpose  of  the  arrangement 
being,  primarily,  to  disclose  the  correlations  or  laws  of 
union  of  properties  and  circumstances,  and,  secondarily, 
to  facilitate  the  operations  of  the  mind  in  clearly  con- 
ceiving and  retaining  in  memory  the  characters  of  the 
objects  in  question." 

A  scientific  classification  is  ordinarily  designed  to 
serve  the  purposes  here  enumerated,  but  there  may  be 
cases,  especially  in  everyday  life,  where  our  primary 
interest  is  not  in  getting  a  -complete  knowledge  of 
things,  but  in  getting  together  things  which  have  a  re- 
lation to  some  common  purpose  or  problem ;  and  in  such 
cases  the  grouping  together  of  things  which  are,  in 
most  respects,  very  dissimilar,  may  be  justifiable. 
Custom-house  regulations,  for  example,  proverbially 
group  together  things  which,  apart  from  certain  eco- 
nomic considerations,  may  be  totally  unlike.  The  so- 


DIVISION  -  37 

called  artificial  classification  may  be  entirely  satisfac- 
tory as  an  index  or  diagnostic  classification,  though  in 
a  diagnostic  classification,  as  we  have  seen,  the  use  of 
essential  qualities  would  furnish  a  surer  means  for  iden- 
tifying doubtful  cases  than  the  use  of  obvious  qualities. 

Classification,  of  whatever  sort,  is  not  simply  bring- 
ing together  data  into  a  single  group ;  it  involves  the 
further  ordering  of  the  data  in  sub-groups. 

Division. — Breaking  up  the  group  into  sub-groups 
is  known  in  logic  as  "  Division."  The  first  thing  to  do 
in  making  a  logical  division  is  to  select  some  charac- 
teristic which  will  serve  to  distinguish  some  members 
of  the  group  from  the  rest.  It  may  belong  to  some 
and  not  to  others,  or  it  may  belong  to  all  in  different 
degrees,  etc.  The  technical  name  of  a  character  used 
for  this  purpose  is  fundamentum  divisionis,  or  basis 
of  division.  The  simplest  sort  of  division  is  that  in 
which  the  fundamentum  divisionis  is  a  character  pres- 
ent in  some  members  of  the  class  and  lacking  in  the  rest. 
Material  substances  may  be  divided  into  those  which 
are  mineral  and  those  which  are  not;  or,  to  cite  an 
ancient  example,  we  may  divide  and  subdivide  sub- 
stances as  follows : 5 

Substance 

A " 


Corporeal     Incorporeal" 


f  \ 

Animate     Inanimate 

A  _ 


t  "S 

Sensible     Insensible 


f  \ 

Rational  Irrational,  etc. 

5  This  is  known  as  the  Tree  of  Porphyry,  so-named  from  the 
Greek  logician  who  was  the  earliest  writer  to  give  a  distinct  ac- 
count of  this  type  of  division. 


38 


CLASSIFICATION 


Division  of  this  kind  is  called  dichotomous  or  bifur- 
cate, from  the  fact  that  each  group  or  sub-group  is 
always  divided  into  two. 

A  more  complex  classification  results  from  selecting 
as  the  basis  of  division  some  character  which  is  pos- 
sessed by  all  the  members  of  the  class  but  with  differ- 
ences of  degree  or  quality,  etc.  Books,  for  example, 
if  classified  according  to  subject  matter,  would  fall  into 
several  groups,  and  each  of  these  might  again  be  sub- 
divided into  several  more.6  A  dichotomous  division 

e  As  further  examples  of  classification  of  this  kind  we  may  cite 
the  following  from  Hy slop's  Logic,  pages  96,  97. 


Figures  - 


Plane., 


Solid, 


Rectilinear . 


.  Curvilinear. 


Rectilinear. 


Curvilinear. 


Mechanical . 


Science . 


Physical, 


Moral , 


[  Trilateral 
]  Quadrilateral 
I  Multilateral 

Circular 
Elliptical 
Parabolic 
Hyperbolic 

Tetrahedrons 
Pentahedrons 
Cubes 
Parallelepipeds,  etc. 

Spheres 
Cones 
Cylinders 
Paraboloids 

{Physics 
Chemistry 


I  Organic {  Biology 

\  Physiology 

f  History 
[Polltlcal {Sociology 

f  Noetics 

Psychological.  -!  Aesthetics 
[  Ethics 


DICHOTOMOUS    DIVISION  39 

would,  of  course,  be  possible  here ;  we  might  have  some- 
thing like  the  following: 

Books 


On  history          Not  on  history 


r  \ 

On  chemistry  Not  on  chemistry,  etc. 

But  a  dichotomous  division  would  soon  become  un- 
wieldly ;  moreover,  it  does  not  present  the  classes  in  such 
a  way  as  to  indicate  which  are  coordinate.  The  ex- 
ample just  given  might  seem  to  make  history  coordi- 
nate with  all  other  subjects  taken  together,  and 
chemistry  might  seem  to  be  subordinate  to  history.  It 
is  desirable,  usually,  that  the  classification  shall  put 
coordinate  classes  on  the  same  plane,  and  this  the 
dichotomous  division  cannot  do. 

Moreover,  this  sort  of  division  embodies  very  little 
information ;  it  points  out  a  class  which  has  a  certain 
character  and  another  which  lacks  it;  the  latter  is  de- 
scribed in  negative  terms  only.  The  other  type  of 
classification  presents  a  number  of  classes,  each  de- 
scribed in  terms  of  some  positive  quality.  Still  there 
are  many  cases  in  which  interest  centers  in  those  mem- 
bers of  a  class  which  possess  (or  lack)  some  certain 
character.  For  some  purposes  the  division  of  popula- 
tion into  voters  and  non-voters,  or  into  literate  and 
illiterate,  may  be  quite  as  satisfactory  as  any  other. 

Sometimes  our  information  regarding  a  class  is  so 
imperfect  that  a  dichotomous  division  is  the  only  one 
we  can  use,  In  a  given  shipload  of  immigrants  we 
might  know  that  some  were  Italians  ?  and  know  nothing 


40  CLASSIFICATION 

about  the  nationality  of  the  rest  except  that  they  were 
not  Italians.  Or  it  might  be  that  those  outside  the 
class  positively  characterized  had  so  little  in  common 
that  no  class  or  series  of  classes,  coordinate  with  the 
first,  could  include  them  all:  the  chemist's  division  of 
elements  into  metals  and  non-metals  illustrates  this. 

It  has  often  been  said  that  a  dichotomous  division  is 
the  only  one  which  insures  against  the  omission  of  any 
individual.  Every  member  of  a  class  must  either  pos- 
sess a  certain  quality  or  be  without  it ;  all  that  are  ex- 
cluded from  the  first  class  are  necessarily  included  in 
the  second,  while  in  the  other  sort  of  division  it  is  easy 
to  overlook  something.  But  if  many  classes  are  to  be 
included,  the  dichotomous  division  soon  becomes  almost 
unmanageable,  and  if  it  is  not  carried  out  to  the  end 
we  will  not  discover  every  class,  although  all  are  for- 
mally included.  If  it  is  carried  out  exhaustively,  every- 
thing will  of  course  be  identified ;  but  the  same  would 
be  true  of  any  other  type  of  classification.  Jevons 
holds  that  diagnostic  classifications  should  usually  be 
dichotomous. 

Requirements  of  Classification. —  In  any  scientific 
classification  (1)  the  sub-classes  must  include  all  that 
is  included  in  the  main  class;  and  (2)  they  must  not 
overlap,  i.  e.,  no  individual  should  belong  to  two  classes 
at  once.  To  classify  people  as  large  and  small  would 
violate  the  first  of  these  rules,  while  to  classify  them  as 
large,  small,  and  blue-eyed,  would  violate  both.  Viola- 
tion of  the  first  rule  results  in  incomplete  division ; 
violation  of  the  second,  in  cross-division. 

Incomplete  division  is  a  consequence  of  failure  to 
carry  out  a  division  to  the  end ;  sometimes  the  principle 


FAULTY    CLASSIFICATION  41 

of  division  does  not  seem  to  permit  this,  or  some  of  the 
data  included  may  be  of  so  peculiar  a  character  that 
they  do  not  seem  to  fall  into  any  well-marked  classes, 
An  escape  from  difficulties  is  sometimes  found  in  a 
miscellaneous  class,  which  shall  include  all  cases  not 
otherwise  provided  for.  When  this  is  employed,  the 
classification  is  certain  to  include  all  cases.  The  mis- 
cellaneous class  corresponds  to  the  negative  class  in 
dichotomous  division. 

Cross-division  is  a  consequence  of  employing  more 
than  one  fundamentum  divisionis.  In  the  example 
above,  both  size  and  eye-color  were  employed  as  bases 
of  division. 

Every  classification  should  be  complete  or  exhaustive ; 
it  should  provide  a  place  for  every  item.  But  a  sort  of 
cross-division  may  sometimes  be  very  useful,  as  in  index 
or  diagnostic  classifications.  Ordinary  subject  indexes, 
classification  of  books  under  author  and  subject,  or  of 
college  courses  under  department  and  year,  are  cases 
in  point,  as  is  also  the  classification  of  a  disease  under 
ea-ch  of  its  several  symptoms. 

A  class  which  is  divided  into  sub-classes  is  technically 
called  a  genus;  while  each  of  the  sub-classes  is  a  species. 
"  Caucasian  "  is  a  species  of  the  genus  "  man."  If  a 
sub-class  were  to  be  divided  it  would  be  a  genus  in  rela- 
tion to  its  sub-classes :  Slavs  are  a  species  of  the  genus 
Caucasian.  Any  class,  then,  regarded  as  inclusive  of 
other  classes  is  a  genus,  whereas  if  it  is  regarded  as 
subordinate  to  some  higher  class  it  is  a  species.  A 
class  which  is  so  wide  that  no  other  can  contain  it  is 
called  a  summum  genus  or  highest  genus ;  it  alone  can 
never  be  a  species.  A  class  which  includes  so  little  that 


42  CLASSIFICATION 

it  can  not  be  subdivided  is  an  infima  species  or  lowest 
species ;  it  can  never  become  a  genus. 

An  individual  which  is  so  unique  that  it  can  be  in- 
cluded in  no  class  whatever  is  sui  generis. 

Under  ordinary  conditions  there  is  little  use  for  these 
last  three  terms.  It  may  be  doubted  whether  there  is 
such  a  thing  as  an  individual  thing  sui  generis,  and 
whether  there  can  be  more  than  one  summum  genus,  or 
any  infima  species  which  is  not  a  class  of  one  member 
only.  In  any  given  investigation  they  may  be  employed 
in  a  relative  sense.  For  anthropology,  mammal  might 
be  regarded  as  the  summum  genus;  and  an  individual 
whose  peculiarities  defy  all  attempts  at  classification  on 
usual  lines  might  be  spoken  of  as  sui  generis;  a  species 
which  could  not  usefully  be  divided  might  be  regarded 
as  an  infima  species.  But  this  use  of  the  terms  would 
not  be  entirely  accurate. 

The  use  of  genus  and  species  as  described  above  is 
the  traditional  logical  usage ;  but  in  the  biological  sci- 
ences they  are  used  in  a  different  sense.  In  those  sci- 
ences the  terms  are  not  relative ;  a  class  is  not  a  species 
at  one  time  and  a  genus  at  another.  Homo  is  always  a 
genus ;  formerly  it  was  thought  to  have  two  species,, 
man  and  the  chimpanzee,  but  now  man,  homo  sapiens, 
is  regarded  as  the  only  species  in  the  genus.  The  Cau- 
casian race  is  a  variety  under  the  species,  homo  sapiens. 
Homo  is  included  in  the  order,  primates,  etc. 

EXERCISES 

1.  What  is  classification? 

2.  What  is  an  Index-classification?     What  is  its  purpose 


EXERCISES  43 

and  on  what  sort  of  quality  is  it  based?  How  would  you 
construct  ait  Index-classification  of  the  rulers  of  Europe 
during  the  Nineteenth  Century? 

3.  What  is  a  Diagnostic-classification?     State  its  purpose 
and  its  principles.     How  would  you  construct  a  classifica- 
tion which  would  serve  for  the  identification  of  birds? 

4.  What  is  the  purpose  of  classification  as  used  in  scien- 
tific work?      What  is   the   difference  between  an   artificial 
and  a  natural  classification? 

5.  What   is   a   Dichotomous   Division,   and  what  are   its 
strong  and  weak  points?     Make  a  dichotomous  division  of 
educational  institutions.     What  is  a  cross-division?      How 
is  it  caused,  and  when  may  it  be  useful  ?     Give  examples  of 
a  genus,  a  species,  a  summum  genus,  an  infima  species,  a 
thing  sui  generis.     Contrast  the  biologist's  use  of  "  genus  " 
and  "  species  "  with  the  more  general  logical  usage. 

6.  Criticise  the  following  classifications  and  divisions: 
a  Men  may  be  classified  as  white  and  colored. 

b  Trees,  as  fruit-trees,  shade-trees  and  forest-trees. 

c  The    fine    arts,    as     sculpture,    painting,    drawing, 
architecture,  poetry  and  photography.   (Fowler.) 

d  Books,  as  those  on  history,  science,  poetry,  religion 
and  belles-lettres. 

e  Political  parties,  as  conservative  and  radical. 

/  The  states  of  New  England,  as  Maine,  New  Hamp- 
shire, Vermont,  and  Connecticut. 

g  Mind,  into  intellect,   feeling  and  will. 

h  Body,  into  extension,  weight,  resistance,  etc.     (Mel- 
lone.) 

i  Religious,  into  monotheistic  and  polytheistic. 

j  Americans,  into  white,  black  and  foreign-born. 

Ic  Politicians,  into  honest  and  dishonest. 

I  Books,  into  dull  and  interesting. 

m  Games,  into  those  which  are  athletic  and  those  which 
are  intellectual. 

n  Pictures,  into  paintings,  engravings,  posters  and  pen 
and  ink  sketches. 

o  Domestic  animals,  into  those  which  are  useful  and 
those  which  are  pets. 

p  Motion,  into  molecular  and  molar. 

^  Bodies,  into  light,  heavy,  and  dense. 


44  CLASSIFICATION 

r  Men,  into  those  whose  main  pre-occupation  is  to  get 
through  time  and  those  whose  aim  it  is  to  find 
time  for  all  that  has  to  be  got  through. 
Can  you  state  circumstances  in  which  any  of  the  above 
might  be  useful  and  satisfactory? 

7.  Divide  and  sub-divide:     Propositions,  Athletic  sports, 
College  publications,  Government,  Poetry,  Furniture,  Races, 
Schools. 

8.  Criticise  the  classing  together  of  negroes,  coal,  and 
black  chalk  on  the  ground  that  they  are  similar  in  being 
black,  solid,  extended,  divisible,  heavy,  etc.     (MeHone.) 


CHAPTER    IV 
THE    USE    AND    MISUSE    OF    WORDS 

Discrimination,  Conception,  Abstraction. — It  will  be 
remembered  that  a  thing  is  put  into  a  given  class  by 
virtue  of  its  possession  of  some  quality  or  relation,  a 
class  being  simply  a  group  of  things  which  have  in 
common  one  or  more  qualities  or  relations.  Any  given 
thing  might,  therefore,  be  classified  in  several  different 
ways.  Bucephalus,  for  example,  might  be  classified  as 
a  horse,  or  as  a  colored  object,  or  as  a  consumer  of 
hay,  or  as  a  possession  of  Alexander  the  Great,  and  so 
on.  Indeed,  most  concrete  objects  might  be  classified 
in  hundreds  of  ways.  For  every  characteristic  which  a 
thing  possesses  there  may  be  a  class,  and  the  way  in 
which  we  shall  classify  it  in  any  given  instance  will 
depend  upon  the  purpose  we  have  in  view.  For  his 
teacher  the  small  boy  is  a  pupil;  for  the  cat,  a  source 
of  danger,  and  so  on.  And  each  mode  of  classification 
is  correct  in  its  place. 

But  before  an  object  can  be  classified  in  a  given  way 
it  is,  of  course,  necessary  to  note  what  qualities  it  does 
possess.  Ordinarily  we  note  very  few  of  these.  Most 
of  us  see  only  the  most  obvious  and  striking  qualities  of 
things,  and  we  often  see  those  very  imperfectly.  We 
get  a  vague  general  impression  and  fail  to  analyse  it 
into  its  elements.  The  child,  in  his  earliest  experiences, 
hardly  discriminates  the  different  qualities  of  a  thing 
at  all,  for  his  first  experiences  are  very  much  confused. 

45 


46      THE    USE    AND    MISUSE    OF    WORDS 

We  know  things  only  as  we  know  their  qualities  and 
relations,  and  the  better  we  can  distinguish  and  relate 
these  the  better  we  know  the  object.  Analysis  of  the 
concrete  datum  is  presupposed  in  classification  and  in 
all  the  other  higher  manifestations  of  consciousness. 

When  we  analyse  a  thing  we  pick  out  its  various  ele- 
ments and  think  of  them  as  more  or  less  isolated  from 
the  complex  in  which  they  were  perceived.  We  can 
think  of  greenness  or  roundness  without  thinking  of 
size  or  hardness  or  of  any  of  the  other  qualities  with 
which  greenness  or  hardness  always  occurs.  We  never 
perceive  greenness  or  hardness  by  themselves,  but  we 
can  think  of  them  without  taking  into  account  the  other 
qualities.  The  mental  act  whereby  we  think  of  them  in 
that  way  cannot  be  perception ;  nor  can  it  be  memory, 
for  memory,  like  perception,  is  of  concrete  complex 
things,  whereas  these  qualities  are  simple  and  abstract. 
The  mental  act  in  which  we  bring  before  ourselves  a 
simple  quality  is  conception;  and  the  thought  of  the 
quality  is  a  concept.  We  have  concepts  of  abstract 
qualities,  but  we  cannot  have  percepts  of  them.  But 
we  may  also  have  concepts  of  concrete  things.  Our 
idea  of  some  particular  horse,  say  Bucephalus,  is  not 
a  memory,  nor  is  it  a  perception ;  it  is  a  concept.1  We 
may  also  have  concepts  of  things  which  we  have  per- 
ceived; indeed,  every  perception  involves  conception  as 
well.  We  are  immediately  aware  of  certain  qualities, 
but,  more  than  that,  we  have  an  idea  of  a  complex  whole 
possessing  more  or  less  coherence,  permanence,  etc. 
Whenever  we  think  of  a  class  of  objects,  qualities,  or 

i  Both  Concept  and  Conception  are  used  for  the  idea  of  the 
thing  or  quality. 


CONCEPTS  47 

what  not,  we  do  so  by  means  of  conception.  The 
thought  of  anything  is  a  concept.  Some  concepts  are 
universal,  some  are  particular ;  some  are  concrete,  some 
are  abstract ;  some  are  of  real  things,  some  of  imaginary 
things,  and  so  on.  Everything  that  is  thought  of  is 
thought  of  in  a  concept,  or  rather,  the  thought  of  any- 
thing is  a  concept  of  that  thing. 

In  conceiving  anything  two  elements  are  present: 
the  symbol,  and  its  meaning.  In  the  concept  "  horse  " 
the  symbol  is  the  word  "  horse  " ;  the  meaning  is  the 
sum-total  of  qualities  which  that  word  implies  or  the 
objects  to  which  it  may  be  applied.  The  symbol  is  not 
necessarily  a  word:  we  might  think  of  horses  without 
having  in  mind  the  word.  The  mental  picture  of  a 
horse  might  be  the  symbol.  If  we  were  trying  to  con- 
vey the  idea  of  a  horse  to  a  person  who  did  not  under- 
stand English,  we  might  use  a  drawing  or  imitate  the 
sound  of  galloping,  and  so  on.  In  all  these  cases  the 
meaning  would  be  the  same,  though  the  symbol  would 
not.  The  essential  element  in  the  concept  is  .the  mean- 
ing; so  long  as  that  remains  the  same  we  have  the 
same  concept,  no  matter  what  the  symbol.  The  same 
thoughts  may  be  present  in  two  minds,  one  of  which 
thinks  in  English  and  the  other  in  German,  or  one  of 
which  thinks  in  words  and  the  other  in  mental  pictures. 
The  superiority  of  words  as  symbols  will  be  discussed 
presently. 

It  is  customary  to  treat  logic  as  if  it  dealt  solely 
with  concepts,  judgments  and  inferences;  but  in  treat- 
ing logic  as  a  part  of  scientific  method,  as  a  part  of 
the  science  of  getting  knowledge,  it  will  be  well  to  con- 
tinue to  speak  as  if  we  were  dealing  directly  with  the 


48      THE    USE    AND    MISUSE    OF    WORDS 

facts  and  not  with  mental  counters.  In  other  words, 
logic  may  be  regarded  as  a  science  of  things  as  well  as 
a  science  of  thoughts.  It  deals,  it  is  true,  only  with 
the  most  general  aspects  of  things ;  not  with  their  spe- 
cial qualities,  as  do  the  special  sciences,  such  as  physics, 
etc.  It  has  to  do  with  that  which  is  common  to 
all  fields  of  facts.  In  certain  cases  it  may  be  more 
convenient  to  speak  of  the  concepts  rather  than  of  the 
things  conceived,  as,  for  example,  in  -geometry,  where 
the  things  conceived  are  certain  highly  abstract  rela- 
tions and  the  like ;  but  even  in  such  cases  the  other  way 
of  speaking  would  be  possible. 

Necessity  for  Language. — Mention  has  already  been 
made  of  the  necessity  for  describing  or  in  some  way 
representing  the  things  we  know.  The  means  most  uni- 
versally employed  and  most  completely  developed  is,  of 
course,  language.  A  language,  from  the  point  of  view 
of  logic  and  scientific  method,  is  simply  a  highly  com- 
plex system  of  symbols  for  the  representation  of  all 
kinds  of  objects  and  experiences,  of  the  conclusions 
and  constructions  based  upon  experience,  of  laws,  and 
so  on.  Language,  as  already  noted,  is  a  -condition  of 
all  progress  beyond  the  merest  rudiments  of  knowl- 
edge. It  might  seem  to  be  of  no  use  in  the  field  of 
observation,  but  an  observation  made  for  some  special 
purpose  or  under  experimental  conditions  implies  a 
previous  statement  or  representation  of  the  thing  to  be 
observed.  Memory  includes  a  representation  of  past 
experience  by  means  either  of  a  mental  picture  or  of 
some  other  sort  of  symbol,  such  as  the  name  of  the 
thing.  All  spoken  and  written  evidence,  of  course,  im- 
plies language;  and  inference  involves  the  statement  to 


LANGUAGE  49 

ourselves  of  a  conclusion  from  something  observed  or 
thought  of.  Classification  obviously  requires  the  use 
of  symbols.2  So  important  is  language  for  the  work 
of  thinking  that  logic  has  sometimes  been  defined  as 
a  branch  of  the  study  of  language.  Whately  said  that 
"  Logic  is  entirely  conversant  about  language."  Some 
have  maintained  that  all  growth  in  thought  has  fol- 
lowed the  development  of  language  and  would  have 
been  impossible  without  it ;  in  other  words,  that  lan- 
guage always  precedes  thought ;  that  man  is  intelligent 
because  he  has  language  and  not  vice  versa.  These 
may  be  extreme  views,  but  it  is  certain  that  systematic 
knowledge  cannot  go  far  without  a  coherent  system  of 
symbols,  and  that  language  is  infinitely  superior  to  all 
other  kinds  of  symbols.3  Any  examination  of  the 
processes  by  which  knowledge  is  attained  must  give 
careful  attention  to  the  consideration  of  language. 

If  language  were  perfect,  it  would  not  be  necessary 
to  discuss  it  at  any  length  in  this  connection,  but  its 
imperfections  are  such  as  to  lead  very  often  to  mistaken 
ideas  and  wrong  conclusions.  It  will  be  necessary, 
therefore,  to  examine  language  in  order  to  discover 
these  imperfections  and  the  means  of  avoiding  them. 

Terms. —  A  word  or  group  of  words  stands  as  the 
representative  of  some  thing,  quality,  relation,  action, 

2  Sometimes  the  mental  picture  of  an  individual  may  stand  for 
the  class;  the  image  of  a  tree  may  stand  for  the  class  tree,  but 
when  we  know  the  name  of  the  class  or  kind,  we  usually  represent 
the  class  to  ourselves  by  means  of  the  name.    Mental  pictures  are 
liable  to  vagueness  and  to  modification,  and  it  has  been  shown  that 
scientists,    for   example,   tend   to   represent   things    to   themselves 
almost  exclusively  by  means  of  words,  particularly  as  they  advance 
in  years. 

3  For  a  discussion  of  this  question  see  Stout,  Manual  of  Psy- 
chology, chap.  v. 


50      THE    USE    AND    MISUSE    OF    WORDS 

idea,  and  so  on,  or  some  group  or  combination  of  them. 
Such  a  word  or  group  of  words  is  called  a  term.  A 
term  might  consist  of  any  number  of  words  and  con- 
tain various  subordinate  clauses,  but  if  it  stood  as  the 
symbol  of  some  single  object  of  thought  it  would  still 
be  one  term.  "  Man  "  and  "  The  torch  in  the  hand  of 
the  Statue  of  Liberty  in  New  York  Harbor "  are 
equally  terms,  for  each  stands  for  a  single  object  of 
thought.  The  inevitable  difficulties  with  regard  to  the 
use  of  terms  arise  from  the  fact  that  a  word  or  a 
group  of  words  may  stand  for  more  than  one  thing; 
it  may  have  a  variety  of  meanings  and  is  therefore  liable 
to  misinterpretation.  Most  words  are  used  in  more 
senses  than  one,  so  the  danger  of  confusion  is  always 
present.  There  are  several  causes  for  this  multiplica- 
tion of  meanings.  One  of  the  most  important  is  (1)  the 
tendency  to  use  a  word  in  a  sense  wider  than  the  one  in 
which  it  was  formerly  used,  to  use  it  more  generally,  to 
generalize  it.  Lens  meant  originally  only  a  double  con- 
vex piece  of  glass ;  such  words  as  curve,  acid,  metal, 
salt,  etc.,  illustrate  this  tendency. 

There  is  also  (2)  a  contrary  tendency  to  limit  the  ap- 
plication of  words,  to  use  a  term  in  a  narrower  sense 
than  formerly,  a  tendency  toward  specialization. 
Minister  meant  originally  a  servant;  now  it  means, 
among  other  things,  the  highest  representative  of  a 
state,  one  of  the  most  exalted  "  servants  "  of  a  govern- 
ment. "  Deacon,  bishop,  clerk,  queen,  captain,  general, 
are  all  words  which  have  undergone  a  like  process  of 
specialization.  In  such  words  as  telegraph,  rail,  signal, 
station,  and  many  other  words  arising  from  new  inven- 
tions, we  mav  trace  the  progress  of  change  in  a  lif(v 


SPECIALIZATION    OF    TERMS  51 

time."  The  use  of  Congressman  to  describe  Repre- 
sentatives only,  and  of  Protection  as  a  name  for 
an  economic  policy,  are  further  illustrations  of  the 
process. 

These  tendencies  may  affect  a  word  and  its  deriva- 
tives in  different  degrees  and  different  directions.  Com- 
pare, for  example,  distinguish  and  distinguished; 
dissolve,  dissolute  and  dissolution;  matter  and  material- 
istic; respond  and  responsible;  design,  designer  and  de- 
signing, etc.  The  popular  and  the  technical  uses  of  a 
term  are  usually  different,  one  being  broader  or  nar- 
rower than  the  other;  phenomenon,  sensation,  idea,  are 
illustrations.  Sometimes  a  special  use  of  a  word  is  only 
local,  as  in  dialects,  or  for  a  short  space  of  time,  as  in 
slang. 

In  addition  to  these  tendencies  to  generalize  and  to 
specialize  the  meaning  of  terms  there  is  (3)  another 
by  which  there  is  a  transfer,  of  meaning  to  associated 
objects  or  to  those  which  are  analogous.  The  use  of 
the  word  church  to  designate  a  religious  society,  or  of 
chair  to  indicate  a  presiding  officer,  or  of  bench  to 
stand  for  the  judiciary,  are  illustrations  of  the  trans- 
fer of  meaning  to  associated  objects,  and  such  expres- 
sions as  a  dull  student,  a  hard  examination,  a  brilliant 
game,  etc.,  illustrate  the  transfer  to  analogous  objects. 

There  are  (4)  some  other  cases  of  less  importance: 
sometimes  two  words  which  were  originally  different  and 
of  different  derivations  are  alike  in  sound  and  spelling 
and  might  possibly  be  mistaken  for  each  other ;  such 
as,  mean  in  the  sense  of  middle  and  mean  in  the  sense 
of  low;  pound  :n  the  sense  of  weight  and  pound  meaning 
a  pen,  pen  as  an  inclosurc  and  pen  as  an  instrument  of 


52     THE    USE    AND    MISUSE    OF    WORDS 

writing,  etc.  Sometimes  words  are  alike  in  sound  but 
different  in  spelling,  as  right,  wright  and  rite,  or  rain 
and  reign;  in  other  cases  they  are  alike  in  spelling  but 
different  in  sound,  as  lead,  the  metal,  and  lead,  some- 
thing to  be  followed,  etc.4  These  last  three  cases  are 
of  little  importance  since  the  confusions  resulting  are 
usually  of  only  momentary  duration.  In  the  first  three 
cases,  those  of  generalization,  specialization  and  trans- 
fer of  meaning,  the  confusion  results  from  the  con- 
tinued use  of  a  word  in  the  older  sense  after  its  meaning 
has  been  extended  to  a  new  field. 

If  the  various  meanings  are  clearly  distinguished  and 
widely  separate,  the  context  will  usually  make  clear 
which  is  intended ;  but  the  meanings  are  most  frequently 
very  similar  or  closely  connected,  otherwise  the  same 
word  would  never  have  been  used  for  both.  The  serious 
consequences  of  these  confusions  are  seen  in  the  fact 
that  so  many  disputes  and  differences  of  opinion  result 
from  a  difference  in  the  use  of  terms. 

Kinds  of  Terms. —  1.  SINGULAR  AND  GENERAL. — We 
have  discussed  the  causes  of  ambiguity  in  terms ;  it  will 
be  well  to  examine  some  of  the  different  kinds  of  terms 
in  order  to  discover  just  what  sorts  of  confusion  are 
likely  to  be  found.  There  are  some  words,  such  as 
proper  names,  which  would  not  seem  liable  to  ambi- 
guity since  they  usually  have  little  or  no  meaning;  but 
after  all  there  may  be  uncertainty  enough  with  regard 
to  the  application  of  the  name,  as  every  case  of  mis- 
taken identity  shows. 

Proper  names  are  simply  one  variety  of  INDIVIDUAL 

4  Most  of  the  illustrations  used  in  the  two  pages  above  have 
been  taken  from  Jevons,  Lesson  in  Logic. 


SINGULAR    AND    GENERAL    TERMS      53 

or  SINGULAR  terms.  "  The  first  president  of  the  United 
States  "  is  quite  as  definite  in  its  application  as  any 
proper  name  could  be.  A  singular  term  is  a  term  which 
can  be  applied,  in  a  given  sense,  to  one  single,  indi- 
vidual object  only.  On  the  other  hand  there  are  terms 
which  may  be  applied  in  the  same  sense  to  an  indefinite 
number  of  objects.  Man,  president,  book,  college,  etc., 
are  GENERAL  terms.  A  term  which  was  originally  sin- 
gular may  become  general,  as  illustrated  in  the  expres- 
sions, "  A  Daniel  come  to  judgment,"  "  A  Homer,"  "  A 
Hannibal,"  etc.  On  the  other  hand  singular  terms 
may  be  so  combined  as  to  apply  to  only  one  individual ; 
the  first  president,  the  wisest  man  in  the  world,  the 
longest  river,  the  highest  mountain,  etc.,  are  such 
cases. 

The  chief  difficulty  in  the  case  of  singular  terms  is 
the  liability  to  error  with  regard  to  the  individual  to 
whom  the  name  applies.  The  form  or  the  context  usu- 
ally shows  clearly  enough  whether  a  term  is  singular 
or  general. 

In  the  case  of  general  terms  there  is  much  more  diffi- 
culty: in  the  first  place  the  meaning  may  be  vague; 
the  application  of  the  term  may  not  be  definite;  in  the 
case  of  such  words  as  rich  and  poor,  wise  and  ignorant, 
and  a  great  many  others,  there  is  no  universal  agree- 
ment and  there  is  seldom  a  definite  notion  as  to  tho 
range  of  application  in  any  particular  case.  Again, 
where  the  term  has  a  plurality  of  applications,  each  of 
which  may  be  sufficiently  definite,  the  wrong  one  may  be 
employed  or  understood  in  any  given  case.  The  word 
law,  for  example,  means,  in  one  field,  a  prescribed  rule 
of  action,  something  imposed  from  without  and  having 


54      THE    USE    AND    MISUSE    OF    WORDS 

a  binding  force,  as  a  civil  law.  In  the  natural  sciences, 
on  the  other  hand,  a  law  is  simply  a  statement  of  the 
way  in  which  things  do  invariably  behave.  Obviously, 
one  who  carries  over  into  the  consideration  of  natural 
phenomena  the  conception  of  law  employed  in  legal 
practice,  is  liable  to  have  a  very  mistaken  view  of 
Nature.  There  is  a  multitude  of  terms  in  which  such 
differences  are  to  be  found.  The  Latin  lex  meant  origi- 
nally something  fixed  or  set,  so  both  these  meanings 
might  be  regarded  as  specializations  in  different  direc- 
tions of  the  original  meanings.  In  other  cases  one 
meaning  is  obviously  more  or  less  general  than  the 
other.  In  the  commandment,  "  Thou  shalt  not  kill," 
the  word  kill  is  obviously  less  general  than  is  the  state- 
ment, "  To  kill  is  to  deprive  of  life";  or  again,  the 
words  rest,  sleep,  etc.,  are  not  intended  to  cover  all 
possible  cases  in  the  statement,  "  Rest,  food  and  sleep 
are  necessary  to  life."  Any  mistake  as  to  the  exact 
sense  in  which  a  word  is  used  will  be  certain  to  lead  to 
mistaken  opinions. 

2.  CONCRETE  AND  ABSTRACT  TERMS. — This  brings 
us  to  the  distinction  between  concrete  and  abstract 
terms,  or  between  terms  used  in  an  abstract  sense  and 
the  same  terms  as  used  in  a  concrete  sense. 

An  abstract  term,  as  the  name  implies,  stands  for 
something  which  is  the  product  of  abstraction;  it  is 
something  separated  from  its  context  and  considered  by 
itself.  For  example,  qualities  are  known  only  as  they 
occur  in  an  object,  in  a  complex  something  which  in- 
cludes many  other  qualities.  We  have  already  seen  that 
these  qualities  are  not  recognized  as  separate  things  in 
the  child's  earliest  experience. 


ABSTRACT    TERMS  55 

If  a  quality  always  appeared  in  the  same  setting,  it 
would  never  be  discriminated  and  hence  could  never  be 
abstracted.  To  quote  Professor  James's  illustration, 
if  all  wet  things  were  cold  and  all  cold  things  were 
wet,  we  should  never  distinguish  coldness  from  wet- 
ness. But  most  qualities  do  occur  in  a  variety  of  set- 
tings and  can  therefore  be  discriminated  and  abstracted. 
When  a  quality  is  abstracted  it  can  be  treated,  for  cer- 
tain purposes,  as  a  separate  thing.  In  studying  color, 
we  disregard  the  other  properties  of  colored  objects 
and  treat  their  -colors  as  something  independent. 

There  are  many  degrees  of  abstraction :  blue  is  ab- 
stract as  related  to  a  blue  object,  but  comparatively 
concrete  as  related  to  color.  An  abstract  term  mav  be 
the  name  of  a  relation,  as  height,  or  an  action,  as 
walking,  or  of  any  characteristic  whatever,  abstracted 
from  its  setting  and  regarded  as  an  independent  thing. 
The  word  which  stands  for  this  characteristic  will  be 
an  abstract  term.  A  given  term  is  often  used  in  both 
senses :  in  the  sentence,  "  Government  is  necessary  to 
civilization,"  the  term  government  is  said  to  be  used  in 
an  abstract  sense ;  in  the  sentence,  "  This  government  is 
a  republic,"  it  is  concrete.  To  confuse  the  more  general 
with  the  less  general  meaning  of  a  term  or  the  abstract 
with  the  concrete  use  of  it,  or  to  argue  from  a  term 
taken  without  qualification  to  the  same  term  qualified 
in  some  particular  way,  is  to  commit  a  fallacy,  the 
Fallacy  of  Accident.  To  conclude  that  it  would  be 
meritorious  to  give  a  beggar  a  dollar  because  charity 
is  a  virtue  would  be  to  commit  this  fallacy.  To  con- 
clude that,  because  the  only  Filipinos  you  have  seen  are 
small,  a  Filipino  is  a  small  person,  would  be  to  commit 


56      THE    USE    AND    MISUSE    OF    WORDS 

what  is  sometimes  called  the  Converse  Fallacy  of  Acci- 
dent; in  this,  we  argue  from  the  concrete  or  the  less 
general  or  what  is  true  in  particular  circumstances,  to 
the  abstract  or  the  more  general  or  to  what  is  true 
apart  from  particular  circumstances. 

The  ancient  example,  "What  is  bought  in  the  mar- 
ket is  eaten ;  raw  meat  is  bought  in  the  market ;  there- 
fore raw  meat  is  eaten,"  illustrates  the  simple  fallacy 
of  Accident.  So  also  does  the  following:  "  The  Greeks 
produced  masterpieces  of  art,  and  as  the  Spartans  were 
Greeks,  they  produced  masterpieces  of  art."  (Davis.) 
"  Greeks,"  in  the  major  premise,  is  used  in  the  generic 
sense.  In  the  minor,  it  has  a  more  specific  meaning. 

To  argue  that  strychnine  should  be  freely  sold  be- 
cause it  is  very  useful  (as  a  medicine)  would  be  to  com- 
mit the  converse  fallacy. 

3.  COLLECTIVE  AND  DISTRIBUTIVE  TERMS. — Another 
distinction  which  is  of  great  importance  in  dealing  with 
terms  is  that  between  collective  and  distributive  terms. 
Army,  for  example,  is  a  collective  term;  it  stands  for 
a  number  of  individuals  taken  together  in  a  group;  it 
is  a  group  term.  A  term  like  man,  on  the  other  hand, 
has  no  such  significance.  It  applies  equally  to  any  and 
every  individual  in  a  class.  In  an  expression  like  all 
men,  for  example,  there  is  danger  of  confusion ;  it 
might  be  taken  to  mean  all  taken  together,  as  in  "  All 
Jiving  men  number  about  1,500,000,000  " ;  or  it  might 
be  used  distributively,  as  in  "  All  men  are  mortal." 
Synonyms  of  the  terms  collective  and  distributive  are 
jointly  and  severally.  Obligations  are  sometimes  laid 
upon  individuals  which  they  are  bound  joiptly  or  sev- 
erally to  observe. 


COMPOSITION    AND    DIVISION  57 

Confusion  between  the  collective  and  the  distributive 
uses  of  a  term  leads  to  the  Fallacies  of  Composition  and 
Division;  arguing  from  the  distributive  to  the  collec- 
tive use  results  in  the  fallacy  of  Composition.  "  Each 
member  of  the  committee  is  insufficiently  informed, 
therefore  the  committee  as  a  whole  is  not  sufficiently 
informed,"  contains  a  fallacy  of  Composition.  But  to 
argue  that  because  a  navy  as  a  whole  was  weak,  the 
individual  ships  were  therefore  weak,  would  be  to  com- 
mit a  fallacy  of  Division.  These  fallacies  should  be 
kept  clearly  distinct  from  the  fallacy  of  Accident.  Here 
we  are  dealing  with  a  group ;  the  question  is,  are  we 
dealing  with  it  simply  as  a  group,  or  are  we  thinking 
of  the  individuals  of  which  it  is  made  up?  In  the  other 
case  we  were  not  concerned  with  a  group  at  all. 

4.  OTHER  KINDS  OF  TERMS. — Various  other  distinc- 
tions might  be  made  among  terms ;  there  is,  for  ex- 
ample, a  distinction  between  positive  and  negative 
terms ;  the  former  being  those  which  imply  the  presence, 
and  the  latter  those  which  imply  the  absence,  of  a  qual- 
ity. White,  just,  warm,  etc.,  illustrate  the  former; 
blind,  empty,  unconscious,  the  latter.  There  is  little 
danger  of  confusion  in  this  and  in  most  of  the  other 
cases  which  might  be  included,  so  we  will  pursue  them 
no  further. 

Definition. — In  any  case  in  which  misunderstanding 
is  likely  to  occur,  the  first  thing  to  do  is,  obviously,  to 
make  clear  what  it  is  that  the  term  stands  for.  In  the 
case  of  a  proper  name  the  application  of  the  term  could 
be  shown  by  producing,  or  pointing  out,  or  describing, 
the  individual  thing  for  which  it  stands,  and  so  of  other 
singular  terms.  But  with  general  terms  that  is  not 


58      THE    USE    AND    MISUSE    OF    WORDS 

possible ;  a  general  term  stands  for  all  possible  cases 
of  a  given  sort,  past,  present  and  to  come,  and  any 
example  or  series  of  examples  could  at  most  illustrate 
the  meaning  of  the  term.  Sometimes  an  example  will 
show  clearly  enough,  for  ordinary  purposes,  what  is 
meant.  But  any  example  might  illustrate  a  variety  of 
things ;  if  two  persons,  each  of  whom  was  entirely  un- 
acquainted with  the  language  of  the  other,  should  try 
to  communicate  by  pointing  to  objects  to  indicate  the 
meaning  of  the  words  they  were  using,  they  would  illus- 
trate the  uncertainty  of  this  method  in  its  extreme  form. 
If  one  of  them  should  point  to  a  horse,  he  might  mean 
any  one  of  a  dozen  different  things:  horse,  or  simply 
animal,  or  useful  animal,  or  large  object,  or  gray,  or 
beautiful,  or  dangerous,  and  so  on.  In  a  minor  degree 
that  sort  of  difficulty  is  always  present  when  illustra- 
tions are  employed  to  indicate  the  meaning  of  terms, 
and  the  method  of  illustrations  is  never  entirely  satis- 
factory. 

In  Plato's  Euthyphro  Socrates  asks  Euthyphro,  who 
claims  to  have  a  precise  knowledge  of  the  subject, 
"  What  is  piety  and  what  is  impiety?  "  The  reply  is, 
"  Piety  is  doing  as  I  am  doing ;  that  is  to  say,  prose- 
cuting any  one  who  is  guilty  of  murder,  sacrilege,  or  of 
any  other  crime — whether  he  be  your  father  or  mother 
or  some  other  person,  that  makes  no  difference ; — and 
not  prosecuting  them  is  impiety."  But  Socrates  is  not 
satisfied  with  this.  "  Remember,"  he  says,  "  that  I  did 
not  ask  you  to  give  me  two  or  three  examples  of  piety, 
but  to  explain  the  general  idea  which  makes  all  pious 
things  to  be  pious."  In  other  words,  what  quality  must 
things  possess  in  order  to  be  called  pious?  When  we 


THE    MEANING    OF    TERMS  59 

ask  for  a  definition  of  a  term  we  wish  to  know  what 
qualities  a  thing  must  have  in  order  to  make  the  term 
applicable. 

It  should  be  noted  that  nearly  all  terms  have  two 
aspects:  they  stand  for  objects  and  they  imply  the 
qualities  which  those  objects  possess.  The  term  man 
stands_for  any  or  all  individual  men,  past,  present  and 
to_come.  It  also  implies  all  the  qualities  which  a  being 
must  possess  in  order  to  be  included  in  the  class.  In 
the  case  of  a  general  term  it  is  obvious  that  all  the  in- 
dividuals for  which  it  stands — in  technical  language, 
its  total  extension — could  never  be  presented.  The  only 
way  of  indicating  the  full  extent  of  its  application  is 
to  show  what  qualities  it  implies,  to  tell  what  its  inten- 
sion is.  That  might  conceivably  be  done  by  enumerat- 
ing all  the  qualities  which  were  regarded  as  essential. 
If  things  in  a  given  group  were  so  unique  that  they 
could  not  be  included  in  a  larger  class,  enumeration  of 
their  qualities  would  be  the  only  way  of  showing  what 
they  were.  But  in  all  ordinary  circumstances,  this  proc- 
ess can  be  abbreviated  by  stating  (1)  the  class  to  which 
the  things  belong  and  (£)  the  quality  which  distin- 
guishes them  from  the  other  members  of  the  class.5 
The  class-name  will  obviously  imply  the  presence  of 

5  "  Definition  "  has  been  variously  defined.  "  Given  any  set  of 
notions,  a  term  jyt  definable  by  means  of  these  notions  when,  and 
only  when,  it  is  the  only  term  having  to  certain  of  these  notions 
a  certain  relation  which  itself  is  one  of  the  said  notions."  (Rus- 
sell, The  Principles  of  Mathematics,  Vol.  I,  chap,  xi,  sec.  108.) 
A  term  is  defined  by  being  given  a  place  in  a  set  of  notions,  which 
place  can  be  occupied  by  it  and  by  it  alone.  Instead  of  being 
assigned  to  a  class  it  is  given  its  place  in  a  complex  system  of 
concepts.  This  last  might  be  regarded  as  the  more  complete  form 
of  definition,  whereas  the  former,  the  traditional  form,  is  less 
complete,  though  adequate  for  ordinary  purposes. 


60      THE    USE    AND    MISUSE    OF    WORDS 

the  qualities  which  these  things  have  in  common  with 
the  others  in  the  class. 

The  class  which  includes  a  thing  is  its  genus:  "  plane 
figure  "  is  the  genus  of  "  triangle."  And  the  quality 
which  distinguishes  it  from  the  other  members  of  the 
class  is  its  differentia  or  peculiar  property;  "  three- 
sided  "  is  the  differentia  of  "  triangle."  A  property  is 
any  essential  quality:  having  an  equal  number  of  sides 
and  angles  would  be  a  property  of  "  triangle."  An 
accident  is  a  quality  which  may  or  may  not  be  present 
in  any  or  all  members  of  a  group :  having  a  right  angle 
is  an  accident  of  "  triangle."  6 

Defects  of  Definitions.— There  are  several  defects  to 
which  definitions  are  liable. 

1.  They  may  be  too  broad,  i.  e.,  they  may  include 
more  than  the  term  is  intended  to  cover.  To  define  a 
square  as  a  rectilinear  figure  would  be  a  case  in  point. 
In  such  definitions  the  differentia  is  not  given  or  not 
properly  given. 

#.  Again,  the  definition  may  be  too  narrow,  that  is, 
it  may  exclude  part  of  what  the  term  is  intended  to 
cover.  To  define  "  American  citizen  "  as  one  born  in 
the  United  States  would  exclude  naturalized  citizens. 
In  this  case  an  accidental  quality  is  taken  as  the  dif- 
ferentia. 

3.  Definitions  are  sometimes  given  in  obscure  or  figur- 
ative or  ambiguous  language.  Dr.  Johnson's  defini- 
tion of  a  network  as  "  anything  decussated  or  reticu- 
lated with  interstices  between  the  intersections  "  is  a 

«  These  four  terms,  genus,  differentia,  property  and  accident, 
together  with  species,  are  what  have  been  traditionally  known  in 
logic  as  the  five  Heads  of  Predicables  or  the  five  ways  in  which 
a  predicate  may  be  affirmed  of  a  subject. 


DEFINITION  61 

favorite  illustration  of  the  obscure  definition,  the  defini- 
tion of  ignotum  per  ignotius.  Spencer's  definition  of 
evolution  as  "  an  integration  of  matter  and  a  concom- 
mitant  dissipation  of  motion ;  during  which  the  matter 
passes  from  an  indefinite  incoherent  homogeneity  to  a 
definite  coherent  heterogeneity;  and  during  which  the 
retained  motion  undergoes  a  parallel  transformation," 
is  sometimes  charged  with  this  fault.  It  should  be  re- 
membered, however,  that  when  a  term  is  to  be  used  with 
scientific  exactness  it  may  be  necessary  to  couch  its 
definition  in  very  technical  terms ;  to  one  who  had  read 
the  discussions  which  lead  up  to  it,  Spencer's  definition 
would  not  seem  obscure.  Figurative  and  ambiguous 
language  should  always  be  avoided  when  exactness  is 
the  aim.  Such  language  may  give  some  suggestion  of 
the  meaning  of  a  term,  but  does  not  really  define  it. 

4.  Sometimes    unessential    attributes    are    employed 
in  defining  a  term :  e.  g.,  "  Books  are  the  things  out  of 
which  libraries  are  made."     Such  definitions  are  obvi- 
ously faulty.     They  use  an  accident  as  the  differentia 
and  do  not  give  the  meaning  of  the  term. 

5.  Whenever   it   is   possible,   a   definition   should  "be 
stated  in  positive  rather  than  negative  terms ;  to  define 
"  an  under-classman  "  as  "  a  student  who  is  not  an  up- 
per-classman "  is  to  tell  what  he  is  not  instead  of  telling 
what  he  is. 

6.  Another  sort  of  bad  definition  is  one  in  which  the 
definition  contains  the  term  to  be  defined  or  some  syno- 
nym or  exact  correlative  of  it.     "  Life  is  that  which 
distinguishes  living  from  non-living  things  "  would  be 
a  flagrant  case ;  "  A  cause  is  that  which  produces  an 
effect  "  is  little  better.    _A  definition  should  state  clearly 


62      THE    USE    AND    MISUSE    OF    WORDS 

the  exact  meaning  of  the  term  to  be  defined.  There  are 
cases,  however,  where  a  complete  definition  is  not  neces- 
sary. Where  the  hearer  is  in  doubt  which  of  two  well- 
known  meanings  is  intended,  or  where  the  term  is  al- 
ready familiar  but  is  used  with  a  slightly  different 
shade  of  meaning,  in  other  words,  where  the  genus  is 
already  known,  the  briefest  indication  of  the  differentia 
may  suffice;  sometimes  the  mention  of  any  accidental 
quality,  or  even  the  use  of  an  illustration,  may  be 
sufficient. 

EXERCISES 

1.  Make  a  list  of  ten  words  which  are  sometimes  misused 
through  the  fact  that  they  have  undergone  generalization; 
a  similar  list  of  those  which  have  undergone  specialization; 
a  list  of  five  in  which  there  has  been  a  transfer  of  mean- 
ing to  arralagous  objects. 

2.  Bring   ten    examples    of   singular   terms    and   ten    of 
general  terms;  five  of  general  terms  which  were  originally 
singular  or  were  derived  from  singular  terms. 

3.  Give  ten  examples  of  collective  terms  and  ten  of  dis- 
tributive.    Show  how  error  might  arise  in  this  connection. 

4.  What   is   a   definition?      Compare   definition    and   de- 
scription.    Define  the  following  terms:    Book,  Party,  Col- 
lege, Republican,  Honesty,  Foot-ball,  Dormitory,  College- 
spirit,  Club,  Money,  Success,  Trustee,  Tariff,  Saint,  Geo- 
metrical figure. 

5.  Criticise  the  following  definitions: 

(1)  A  phonogra»ph  is  a  mechanism  xor  recording  and 

reproducing  sounds. 

(2)  A  sea  is  a  body  of  water,  next  in  size  to  tho 

oceans,  entirely,  or  almost  entirely,  surrounded 
by  land. 

(3)  A  library  is  a  collection  of  books  generally  for 

personal  use  and  not  meant  for  merchandise. 

(4)  A  wagon  is  a  conveyance  mounted  on  wheels  and 

drawn  by  some  animal,  usually  a  horse. 


EXERCISES  63 

(5)  Oxygen  is  the  most  important  gaseous  element 

known,  without  which  combustion  and  animal 
life  would  be  impossible. 

(6)  A   sensation   is   a   modification   of   consciousness 

produced  by  the  excitation  of  a  cortical  cen- 
ter through  the  agency  of  an  afferent  nerve- 
current. 

(7)  "  Life  is  a  continuous  adjustment  of  internal  to 

external  relations." 

(8)  Logic  is  the  Baedeker  of  the  world  of  thought. 

(9)  A  cause  is  that  which  produces  an  effect. 

(10)  A  book  is  a  combination  of  leaves  and  cover. 

(11)  A  sun-dial  is  an  affair  for  telling  time  by  means 

of  the  sun. 

(12)  Public    opinion   is   the   opinion   of   people    gen- 

erally. 

(13)  A   student  is    one   whose    principal   business    is 

study. 

(14)  A  just  judge  is  one  who  never  shows  partiality 

in  his  decisions. 

(15)  Wood  is  the  ligneous  part  of  trees. 

(16)  Football  is   a  game  which  is  usually  played  in 

America  with  a  large  ball  in  the  shape  of 
an  oblate  spheroid,  whereas  in  England  a 
spherical  ball  is  used. 

(17)  A  liar  is  a  man  who  wilfully  misplaces  his  onto- 

logical  predicates. 

(18)  A  philosophical  work  is  one  which  treats  of  some 

metaphysical  subject. 

(19)  A  philosophical  work  is   one  which  deals   with 

something  abstract  and  difficult. 

(20)  A  false  weight  is  an  abomination. 

(21)  The   quality  of   a  proposition   is   what  tells   us 

whether  it  is  affirmative  or  negative. 

(22)  Definition  is  telling  what  a  word  means. 

(23)  A   religion   is    that   which   satisfies    the   highest 

needs  of  man. 

(24)  Matter    is   the    stuff    out    of    which   things    are 

made. 
6.  What  fallacies  are  committed  in  the  following  cases? 


64-     THE    USE    AND    MISUSE    OF    WORDS 

(1)  The  holder  of  some  shares  in  a  lottery  is  sure 

to  gain  a  prize,  and  as  I  am  the  holder  of  some 
shares  in  a  lottery  I  am  sure  to  gain  a  prize. 
(Hyslop.) 

(2)  A   monopoly   of  the   sugar-refining   business   is 

beneficial  to  the  sugar-refiners  j  and  of  the  corn 
trade  to  the  corn  growers;  and  of  silk-manu- 
facture to  the  silk  weavers;  and  of  labor  to 
the  laborers.  Now  all  these  classes  of  men 
make  up  the  whole  community.  Therefore  a 
system  of  restrictions  upon  competition  is 
beneficial  to  the  community.  (Hyslop.) 

(3)  Who  is  most  hungry  eats  most;  who  eats  least 

is  most  hungry;  therefore  who  eats  least  eats 
most. 

(4)  All  the  trees  in  the  field  make  a  dense  shade; 

therefore  this  elm  tree,  which  is  one  of  them, 
makes  a  thick  shade. 

(5)  Cities  are  governed  by  mayors;  hence  a  mayoi 

was  the  highest  official  in  ancient  Rome. 

(6)  The  major  received  a  D.S.O.  for  attacking  the 

enemy  and  appropriating  their  supplies ;  there- 
fore it  is  praiseworthy  to  steal. 

(7)  The    Irish    are   quick-witted;    hence   that    Irish 

policeman  must  be  quick-witted. 

(8)  This  ship  is  one  of  the  best  in  the  world,  for  it 

belongs  to  the  British  Navy,  which  is  the  best 
in  the  world. 

(9)  Americans  are  liberal;  hence  this  man  may  be 

counted  on  to  give  liberally,  since  he  is  an 
American. 

(10)  We  can  now  see  the  results  of  giving  the  negro 

all  the  rights  and  privileges  of  the  white  man. 
Two  months  after  he  was  placed  in  office,  this 
colored  man  absconded  with  all  the  funds  un- 
der his  control. 

(11)  Every  man  has  a  right  to  teach  his  religious  be- 

liefs; therefore  it  is  not  out  of  place  for  a 
college  instructor  to  do  so  in  the  discharge  of 
his  duties. 


EXERCISES  65 

(12)  Any  student  in  college  would  stand  higher  in  his 

class  if  he  received  higher  marks;  hence  if  all 
marks  were  raised  10%  every  man  would 
stand  nearer  the  head  of  his  class. 

(13)  Pine  wood  is  good  for  lumber;  matches  are  pine 

wood;  therefore  matches  are  good  for  lumber. 
(Hyslop.) 

(14)  To  teach  a  child  is  to  improve  him;  showing  him 

how  to  pick  pockets  is  teaching  him;  hence 
that  improves  him. 

(15)  Poisons   cause   death;   nux  vomica  is   a  poison; 

therefore  it  causes  death. 

(16)  This  reformer  was  working  for  selfish  ends  all 

the  time ;  no  more  reformers  for  me. 

(17)  Since   attending   that    socialist   meeting    I    have 

had  no  confidence  in  socialistic  doctrines. 

(18)  He  cannot  be  innocent,  for  he  was  a  member  of 

the  mob  which  committed  the  deed. 

(19)  Those  two  horses  would  make  an  excellent  team, 

for  each  is  the  best  of  its  class. 

(20)  Five  is  an  odd  number;  three  and  two  are  five; 

and  hence  each  is  an  odd  number. 


CHAPTER   V 
PROPOSITIONS 

DIFFICULTIES  in  the  use  of  language  are  not  all  pro- 
vided against  by  the  correct  definition  of  terms.  Many 
arise  in  the  combination  of  words  into  sentences.  A 
term,  as  we  have  seen,  is  the  representative  in  lan- 
guage of  some  object  of  thought,  real  or  imaginary, 
concrete  or  abstract.  But  the  mind  never  rests  in  the 
contemplation  of  a  single  object;  it  always  tends  to 
make  an  assertion  or  judgment  about  this  object. 
Most  logicians  are  now  of  the  opinion  that,  even  in  the 
simplest  perception,  a  judgment  is  either  present  or  im- 
plied. Introspection  will  show  at  once  that  when  we 
hold  an  object  before  the  mind,  there  is  an  inevitable 
tendency  to  think  some  assertion  about  it.  The  ex- 
pression of  this  mental  assertion  or  judgment  in  lan- 
guage is  a  proposition. 

Kinds  of  Propositions. — Propositions  are  usually 
distinguished  according  to  quality  and  quantity.  (1) 
The  qualities  are  two,  affirmative  and  negative.  The 
difference  between  affirmative  and  negative  propositions 
is  sufficiently  familiar.  It  should  be  remembered,  how- 
ever, that  the  mere  occurrence  of  not  or  some  other 
negative  particle  in  a  proposition  does  not  necessarily 
make  the  proposition  negative.  The  proposition, 
"  Those  who  do  not  study  are  in  danger  of  failing," 
is  not  a  negative  proposition.  It  asserts  positively 
something  about  a  certain  class,  namely,  "  those  who 

66 


QUALITY    AND    QUANTITY  67 

do  not  study  " ;  these  words  constitute  a  negative  term. 
An  affirmative  statement  can  be  made  about  a  negative 
subject  as  readily  as  about  any  other.  In  the  proposi- 
tion, "  Those  who  do  not  study  are  unwise,"  the  term 
unwise  is  also  negative,  but  the  proposition  is  affirma- 
tive. To  decide  whether  any  proposition  is  affirma- 
tive or  negative,  determine  whether  something  is 
affirmed  or  denied  of  a  subject.  What  the  subject  is, 
and  what  the  predicate  is,  makes  no  difference ;  the  only 
question  is,  do  we  affirm  something  or  do  we  deny  some- 
thing? (2)  With  regard  to  quantity,  propositions 
may  be  either  universal  or  particular.  A  universal 
proposition  is  one  which  expresses  a  judgment  about 
the  whole  of  the  class  to  which  the  subject  applies. 
"  All  the  stars  are  suns  "  is  a  universal  proposition ;  so 
is  "  No  planets  are  self-luminous."  (The  latter  propo- 
sition is  negative  and  denies  something  of  all  planets.) 
"  Some  stars  are  double  "  is  called  a  particular  propo- 
sition. It  asserts  something  of  some  individuals  of  the 
class  "  stars."  By  "  particular  proposition  "  is  not 
meant  a  statement  about  some  particular  individual. 
The  proposition  "  Jupiter  is  the  largest  of  the 
planets  "  is  not  a  particular  proposition.  It  is  a  sin- 
gular proposition,  but,  since  it  expresses  a  judgment 
about  the  whole  of  that  for  which  the  term  "  Jupiter  " 
stands,  it  may  be  treated  as  a  universal  proposition. 
The  so-called  particular  propositions  are  really  indefi- 
nite; if  the  "  some  "  in  any  proposition  meant  certain 
particular  ones,  as  it  does  in  certain  cases,  the  propo- 
sition would  really  be  universal ;  it  would  say  something 
about  all  those  of  whom  the  assertion  was  made:  as 
"  some  persons  "  (meaning  A,  B,  C)  "  are  certain  to  be 


68 


PROPOSITIONS 


late."  As  used  ordinarily,  some  means  certain  unspeci- 
fied individuals,  it  may  or  may  not  be  all.  The  word 
indefinite  would  certainly  be  more  appropriate  here,  but 
the  word  particular,  with  this  special  meaning,  is  the 
one  which  has  been  used  traditionally. 

With  this  two-fold  distinction  of  quality  and  quan- 
tity we  get  four  different  kinds  of  propositions:  uni- 
versal affirmative,  universal  negative,  particular  affirm- 
ative and  particular  negative.  For  the  affirmative 
propositions  the  letters  A  and  I  are  used  as  symbols, 
A  standing  for  the  universal  affirmative  and  I  for  the 
particular  affirmative.  E  stands  for  the  universal  nega- 
tive and  O  for  the  particular  negative.  (These  letters 
are  from  the  Latin  Affirmo  and  Nego.) 


Propositions 


Quality 


Universal 


Particular 


f  Affirmative 
|  Negative 

f  Universal 
(  Particular 
f  Affirmative  A 
|  Negative  E 

f  Affirmative  I 
1  Negative  O 


Propositions  and  Terms.  The  Relation  of  Subject 
to  Predicate. — The  question  of  the  relation  of  propo- 
sitions and  terms  is  one  that  naturally  arises  here.  A 
proposition  obviously  contains  terms.  Ordinarily  it 
is  said  that  a  proposition  is  made  up  of  two  terms  and 
a  copula.  One  of  these  terms  is  the  subject  and  the 
other  is  the  predicate.  The  copula  is  that  which  con- 


SUBJECT    AND    PREDICATE  69 

nects  subject  and  predicate;  it  is  always  some  part  of 
the  verb  to  be.  Some  propositions  do  not  fall  natu- 
rally into  this  form :  for  example,  "  The  earth  moves." 
This  can,  however,  be  expressed  in  this  form :  "  The 
earth  is  a  body  which  moves." 

This  form,  subject-copula-predicate,  is  called  the 
"  logical  form  "  of  the  proposition.  It  often  seems 
artificial,  but  for  certain  purposes  it  is  convenient  to 
employ  it,  and  the  attempt  to  restate  propositions  in 
this  form  is  an  excellent  way  of  finding  out  just  what 
the  proposition  means. 

The  subject  of  a  proposition  stands  for  that  about 
which  something  is  said.1 

The  predicate  is  that  which  is  asserted  of  the  sub- 
ject. The  copula  is  that  which  connects  the  two  terms 
in  a  proposition;  but  the  nature  of  that  connection  is 
not  always  the  same.  In  the  propositions,  "  Aristotle 
was  the  greatest  pupil  of  Plato,"  "  Aristotle  was  wise," 
"  Aristotle  was  traveling  in  Asia  Minor,"  and  "  Aris- 
totle was  a  philosopher,"  the  copula  has,  in  each  case,  a 
different  meaning.  In  the  first,  the  relation  is  that  of 

1 A  distinction  may  be  made  between  the  grammatical  and 
the  logical  subjects.  The  grammatical  subject  is  the  subject 
of  the  proposition;  it  is,  as  we  have  seen,  a  term.  The  logical 
subject  has  been  variously  defined.  The  definition  of  the  logical 
subject  as  the  subject  of  the  thought  seem,  on  the  whole,  to  be 
the  best.  (See  for  discussion,  Joseph,  Introduction  to  Logic.) 
The  logical  subject  is  that  about  which  the  judgment  is  made. 
For  example,  in  the  proposition,  "  Acid  turns  blue  litmus  paper 
red,"  the  grammatical  subject  is,  of  course,  the  word  "  acid." 
The  grammatical  predicate  is  that  which  stands  for  what  is 
asserted  about  the  subject;  in  this  case,  the  words  "turns  blue 
litmus  paper  red."  Changing  the  proposition  into  the  form  of 
subject-copula-predicate,  it  would  read  "  acid  is  that  which 
turns  blue  litmus  paper  red,"  and  the  complete  predicate  would 
be  the  words  following  the  copula.  Now  the  form  of  the  propo- 
sition may  not  indicate  the  real  logical  subject.  If  the  statement 
just  given  were  the  answer  to  the  question,  "What  can  you  say 


70  PROPOSITIONS 

identity;  in  the  second,  that  of  subject  and  attribute; 
in  the  third,  that  of  agent  and  action;  in  the  fourth, 
that  of  inclusion  of  an  individual  in  a  class.  .Logicians 
have  usually  taken  the  last  of  these  as  the  typical 
relation ;  the  others  can  be  transformed  with  more  or 
less  success  into  it.  The  proposition,  "  Aristotle  was 
wise,"  can  be  put  in  the  form,  "  Aristotle  was  a  wise 
man  " ;  and  "  Aristotle  was  traveling,"  etc.,  can  be  ex- 
pressed in  the  form,  "  Aristotle  was  a  man  who  was 
traveling,"  etc.  These  forms  are  sometimes  criticised 
as  not  expressing  the  exact  shade  of  meaning  contained 
in  the  other  forms ;  but  the  difference  is  usually  not 
serious,  and  the  performance  of  certain  logical  opera- 
tions is  much  facilitated  by  so  expressing  the  judg- 
ment as  t'o  indicate  the  inclusion  of  an  individual,  or  a 
class,  in  another  class. 

In  the  negative  proposition  the  relation  will,  of 
course,  be  that  of  exclusion.  "  Minors  are  not  voters  " 
indicates  the  exclusion  of  the  first  class  from  the 
second. 

about  acid,  the  grammatical  and  logical  subjects  would  cor- 
respond; but  if  the  question  were,  "What  is  the  effect  of  acid 
on  litmus  paper?"  the  logical  subject  (i.  e.,  the  thing  about 
which  the  judgment  is  made)  would  be  that  which  is  expressed 
by  the  grammatical  predicate  of  the  proposition.  The  form  of 
the  sentence  could  be  so  changed  as  to  make  the  grammatical 
or  verbal  subject  correspond  to  the  logical  subject;  in  a  great 
many  cases  they  do  not  so  correspond.  Ordinarily  the  logical 
subject  can  be  determined  only  by  the  context,  though  sometimes 
it  can  be  indicated  by  emphasis  on  certain  words.  For  example, 
"Acid  turns  blue  litmus  paper  red  "  would  imply,  as  the  subject, 
what  is  expressed  by  the  words,  "  the  color  to  which  blue  litmus 
is  turned  by  acid."  Unless  otherwise  specified  the  term  subject 
will  be  understood  to  mean  grammatical  subject;  and 
predicate  will  mean  the  term  that  is  joined  to  the  subject  by 
the  copula.  In  the  treatment  of  isolated  propositions  there  is  no 
occasion  for  the  distinction.  It  is  sometimes  said  that  reality 
as  a  whole  is  the  logical  subject  of  every  judgment.  It  might 
better  be  called  the  ultimate  or  metaphysical  subject. 


DISTRIBUTION  71 

The  Distribution  of  Terms  in  a  Proposition,— There 
are  degrees  of  inclusion  and  exclusion.  In  the  illus- 
tration just  given  the  whole  of  the  class  minors  is  ex- 
cluded from  the  whole  of  the  class  voters.  In  the 
proposition,  "  Some  men  are  not  good  citizens,"  only 
some  men  or  a  part  of  the  class  men  is  excluded  from 
the  class  good  citizens,  but  the  whole  of  the  class  good 
citizens  is  excluded  from  that  part  of  the  class  men 
which  is  included  in  the  subject.  In  the  proposition, 
"  Some  men  are  healthy  animals,"  a  part  of  the  class 
men  is  included  in  the  class  healthy  animals,  and  conse- 
quently a  part  of  the  class  healthy  animals  may  be 
included  in  the  class  men.  Again,  in  the  propo- 
sition, "  All  men  are  bipeds,"  the  whole  of  the  class 
men  is  included  in  the  class  bipeds,  but  so  far 
as  this  proposition  informs  us,  only  a  part  of  the  class 
bipeds  can  be  included  in  the  class  men.  When- 
ever, in  a  proposition,  a  term  is  used  to  indicate 
the  whole  of  the  class  for  which  it  stands,  it  is  said  to 
be  distributed;  when  it  covers  only  a  part  of  the  class, 
it  is  undistributed.  The  subject  of  a  universal  proposi- 
tion is  always  distributed,  because,  by  definition,  a  uni- 
versal proposition  is  one  which  asserts  something  about 
the  whole  of  its  subject.  It  will  be  seen  in  the  examples 
given  above  that  both  the  negative  propositions  dis- 
tribute their  predicates.  That  is  always  the  case  with 
negative  propositions.  They  always  indicate  the  en- 
tire exclusion  of  the  predicate  from  the  subject.  The 
proposition  A,  being  universal  and  affirmative,  will  dis- 
tribute its  subject  but  not  its  predicate;  /,  being  par- 
ticular (indefinite)  and  affirmative,  will  distribute 
neither;  the  particular  negative,  0,  will  distribute  the 


72  PROPOSITIONS 

predicate,  but  not  the  subject,  while  the  universal  nega- 
tive, E,  will  distribute  both  subject  and  predicate. 

Euler's  Method.  —  Euler,  a  Swiss  mathematician  of 
the  Eighteenth  Century,  devised  the  following  method 
of  representing  the  relation  of  subject  and  predicate 
and  the  distribution  of  each.  Let  each  term  be  repre- 
sented by  a  circle  ;  then  the  E  proposition  will  be  rep- 
resented as  follows,  S  standing  for  the  subject  and  P 

for  the  predicate:    (§)(?)•   S   and  P  are  shown  to  be 

entirely  excluded  from  each  other;  each  is  distributed. 
The  A  proposition  would  be  represented  in  this  way: 

,  ---  x  S  is  seen  to  be  entirely  included  in  P,  while,  so 
(  ©P}  ^ar  as  we  know,  only  a  part  of  P  falls  within  S  ; 

sx  __  S  S  is  distributed,  P  is  not.  In  the  I  proposition 
the  circles  would  overlap.  Each  would  be  partially  in- 
\  eluded  within  the  other:  that  is,  neither  would 


1  S  (  )P 

\   y    ./  be  distributed.     Whether  cither  extended  fur- 

ther would  be  left  undetermined  ;  there  are  four  possi- 
bilities, in  each  of  which  at  least  some  S  is  some  P.  In 
the  O  proposition,  part  of  S  would  be  excluded 


SOP 

^— ^-xfrom   P;   the  rest   would  be  left  undetermined; 

while  all  of  P  would  be  outside  the  specified  part  of  S ; 
S  is  not  distributed,  P  is. 

The  distribution  or  non-distribution  of  terms  in  the 
various  propositions  may  be  represented  by  the  follow- 
ing symbols :  "  -  '  indicating  an  affirmative  proposi- 
tion, "  x  "  a  negative  one,  and  a  circle  about  a  term 
the  fact  that  it  is  distributed.2 

A,    ©-P;   E,    (§)  x    ©  ;    I,  S-P;  O,  S  x   (5) 

2  The  last  two  of  these  symbols  are  adapted  from  Hyslop, 
ments  of  Log\\,* 


AMBIGUOUS    PROPOSITIONS  73 

Ambiguous  Propositions. — There  are  several  kinds 
of  ambiguous  propositions.  In  the  first  place  the  ar- 
rangement of  the  words  and  phrases  may  be  such  as 
to  admit  of  two  interpretations.  Familiar  examples 
are  the  prophecy  in  Shakespeare's  Henry  VI,  "  The 
Duke  yet  lives  that  Henry  shall  depose,"  and  the  re- 
sponse of  the  oracle,  "  Pyrrhus,  I  say,  the  Romans  shall 
subdue."  The  expression,  "  Twice  two  and  three,"  is 
ambiguous  for  the  same  reason,  and  so  is  the  state- 
ment, "  He  went  away  and  returned  yesterday."  In 
the  two  last,  punctuation  would,  of  course,  remove  the 
ambiguity.  Propositions,  like  "  He  jests  at  scars  who 
never  felt  a  wound,"  will  sometimes,  mislead  a  careless 
reader.  Care  in  the  construction  of  a  proposition  will 
/obviate  such  difficulties ;  where  such  sentences  are 
found,  only  the  context  can  make  clear  what  the  mean- 
ing is.  Wrong  conclusions  in  such  cases  are  said  to 
result  from  committing  the  Fallacy  of  Amphiboly  or 
Amphibology. 

Certain  other  cases  of  ambiguity  might  be  brought 
under  this  heading.  One  of  these  is  found  in  the  use 
of  "  all  ...  not."  In  the  statement,  "All  these 
men  are  not  swift-footed,"  it  might  be  thought  that  the 
meaning  was,  "  None  of  these  men  is  swift-footed  " ; 
that  is,  that  the  subject,  these  men,  was  distributed,  and 
that_  the  proposition  was  an  E  proposition.  It  is 
usually  interpreted  as  meaning  "  some  are  not  swift- 
footed,"  not  "  all  are."  It  is  an  E  proposition  in  form, 
but  an  O  proposition  in  meaning.  Again,  it  might 
seem  to  imply  that  "  some  are  swift- footed  " ;  but  this 
last  implication  is  not  to  be  trusted,  for  we  could  make 
the  original  statement  if  we  knew  that  some  of  these 


74  PROPOSITIONS 

were  not  swift  without  knowing  anything  about  the 
rest.  The  word  some,  as  already  noted,  is  indefinite ;  in 
an  affirmative  proposition,  such  as  "  Some  are  going," 
it  seems  to  imply  the  corresponding  negative,  "  Some 
are  not  going,"  and  vice  versa ;  but  these  implications 
count  for  nothing  if  not  confirmed  in  some  other  way. 
In  interpreting  a  proposition  the  only  safe  rule  is  to  in- 
clude in  its  meaning  only  what  it  must  mean,  not  what 
it  may  mean. 

In  still  other  cases  it  is  not  so  much  the  arrangement 
as  it  is  the  character  of  the  terms  that  occasions  diffi- 
culty. Propositions  which  are  introduced  by  the  word 
•few  are  ambiguous.  "  Few  are  completely  masters  of 
themselves  "  really  means  that  most  are  not  masters  of 
themselves,  or  that  not  many  are.  It  is  an  O  proposi- 
tion in  meaning,  though  like  an  I  proposition  in  form. 
It  may  also  seem  to  suggest  the  corresponding  I  propo- 
sition, "  Some  are  masters,"  etc.  The  importance  of 
making  clear  the  negative  force  of  such  a  proposition 
may  be  illustrated  thus :  suppose  we  have  also  the  state- 
ment, "  All  who  are  masters  of  themselves  are  mature 
individuals " ;  it  might  seem  that  we  could  conclude 
that  few  are  mature  individuals.  If  the  proposition 
"  Few,"  etc.,  be  put  in  the  negative  form  given  above 
there  will  be  no  temptation  to  draw  the  erroneous  con- 
clusion. Thus  in,  "  Most  men  are  not  masters,  etc. ; 
those  who  are,  are  mature,"  etc. ;  the  conclusion,  "  Most 
men  are  not  mature,"  does  not  even  seem  to  follow. 
Professor  Hyslop,  in  his  Elements  of  Logic,  calls  propo- 
sitions of  this  sort  partitive  propositions,  because  they 
"  express  a  part  of  a  whole  of  which  the  implied  propo- 
sition is  a  complementary  part." 


PARTITIVE    AND    EXCLUSIVE  75 

Another  sort,  similar  in  certain  respects  to  these,  is 
found  in  the  exclusive  propositions;  they  are  such  as 
have  their  application  determined  by  such  expressions 
as  only,  alone,  none  but,  and  the  like.  "  None  but 
native-born  citizens  are  eligible  to  the  presidency," 
"  Only  students  will  be  admitted,"  etc.,  are  exclusive 
propositions.  These  statements  do  not  mean  that  all 
native-born  citizens  are  eligible  nor  that  all  •  students 
will  be  admitted.  They  are  not  universal  propositions ; 
they  do  not  distribute  their  subjects.  They  are  equiva- 
lent to  the  propositions,  "  Those  who  are  not  native- 
born  are  not  eligible,"  "  Those  who  are  not  students 
will  not  be  admitted,"  which  are  the  complementary 
opposites  of  the  original  propositions,  and  are  in  this 
case  E  propositions.  As  the  original  propositions  stand 
they  really  limit  the  application  of  their  predicates, 
i.  e.9  they  include  the  whole  of  the  predicate  in  the  sub- 
ject. Thus  they  distribute  the  predicate,  in  spite  of 
the  fact  that  they  are  affirmative  propositions.  They 
are,  therefore,  exceptions  to  the  rule  for  affirmative 
propositions  (p.  71).  Another  way  of  restating  ex- 
clusive propositions  is  to  convert  them,  making  the 
converse  a  universal  proposition.  Thus  :  "  All  persons 
eligible  to  the  presidency  are  native-born  citizens  " ; 
"  All  who  are  to  be  admitted  are  college  students." 

One  other  sort  of  proposition  of  this  general  class 
may' be  mentioned,  the  exceptive  proposition:  it  is  in- 
troduced by  such  words  as  "  All  except,"  "  all  but," 
etc.  For  example :  "  All  but  the  best  will  be  excluded." 
In  addition  to  the  positive  statement,  a  corresponding 
negative  is  suggested,  namely,  "  The  best  will  not  be  " ; 
though  this  last  is  not  certainly  true.  It  is  well  to  re- 


76  PROPOSITIONS 

state  such  propositions,  eliminating  the  exceptive  par- 
ticle. Thus :  "  All  those  who  are  not  the  best,"  etc. 

Figurative  statements  are  peculiarly  liable  to  mis- 
interpretation ;  Hyperbole  and  metaphor,  symbolical 
and  allegorical  statements,  may  all  be  mistaken  for 
literal  statements,  or  if  recognized  as  figurative,  they 
may  be  wrongly  interpreted  on  account  of  the  inherent 
vagueness  of  most  figurative  expressions.  Fallacies 
arising  from  this  cause  are  known  as  Fallacies  of  Figure 
of  Speech.3 

Another  source  of  ambiguity  and  misinterpretation 
in  propositions  is  to  be  found  in  misplaced  emphasis. 
Wrong  emphasis  gives  rise  to  what  is  known  as  the 
Fallacy  of  Accent.  To  quote  from  Jevons :  "  It  is  cu- 
rious to  observe  how  many  and  various  may  be  the 
meanings  attributable  to  the  same  sentence  according 
as  emphasis  is  thrown  on  one  word  or  another.  Thus 
the  sentence,  '  The  study  of  Logic  is  not  supposed  to 
communicate  the  knowledge  of  many  useful  facts,' 
may  be  made  to  imply  that  the  study  of  Logic  does 
communicate  such  a  knowledge  although  it  is  not  sup- 
posed to  do  so ;  or  that  it  communicates  a  knowledge 
of  a  few  useful  facts ;  or  that  it  communicates  a  knowl- 
edge of  many  useless  facts.  .  .  .  Jeremy  Bentham 
was  so  much  afraid  of  being  misled  by  this  fal- 
lacy of  accent  that  he  employed  a  person  to  read  to 
him,  as  I  have  heard,  who  had  a  peculiarly  monotonous 
manner  of  reading."  To  introduce  italics  into  a  quo- 
tation, with  no  mention  of  the  fact  that  they  did  not 

3  It  has  been  said  that  some  of  Locke's  erroneous  conclusions, 
in  his  Essay  on  the  Human  Understanding,  resulted  from  his  own 
use  of  "  the  sheet  of  white  paper  "  as  a  figure  representing  the 
mind  before  experience  has  begun. 


THE    FALLACY    OF    ACCENT  77 

occur  in  the  original,  is  usually  to  misrepresent  the 
meaning  of  the  original.  De  Morgan  and  others  have 
pointed  out  that  taking  words  or  passages  out  of  their 
context  may  have  the  same  consequences.  Isolated 
texts  from  sacred  writings  are  often  misused  in  this 
way ;  e.  g.,  "  Eat,  drink  and  be  merry,  for  to-morrow 
ye  die,"  "Take  no  thought  for  the  morrow,"  etc. 

Quoting  an  argument  which  an  author  has  presented 
only  in  order  to  refute  it,  without  mention  of  his  pur- 
pose, is  another  case  of  the  same  sort. 

EXERCISES 

1.  In  each  of  the  following  propositions  give  (a)  the 
complete  subject  and  (b)  the  complete  predicate;  (c)  re- 
state each  in  its  logical  form;  (d)  give  its  quantity  and 
quality  and  the  letter  which  symbolizes  it.  And  state 
whether  (e)  the  subject  and  (f)  the  predicate  are  dis- 
tributed. , 

(1)  He  laughs  best  who  laughs  last. 

(2)  Few  are  able  to  endure  such  hardships. 

(3)  Not  all  who  are  called  are  chosen. 

(4)  Nothing  of  worth  is  without  honor. 

(5)  Only  genius  could  have  accomplished  it. 

(6)  He  little  knows  you,  who  can  speak  of  you  in 

such  terms. 

(7)  Every    bit    of    success    makes    further    success 

easier. 

(8)  Like  cures  like. 

(9)  There  is  nothing  either  good  or  bad  but  thinking 

makes  it  so. 

(10)  It  is  the  first  step  that  costs. 

(11)  Everything  has  its  limit. 

(12)  We  demand  non-partisan  judges. 

(13)  His  lack  of  enterprise  cost  him  his  position. 

(14)  The  plowman  homeward  plods  his  weary  way. 

(15)  Contentment  is  better  than  riches. 

(16)  Every  deed  returns  upon  the  doer. 

(17)  All's  fair  in  war, 


78  PROPOSITIONS 

(18)  Many  a  morning  on  the  moorland  have  we  heard 

the  copses  ring. 

(19)  Perfection  is  beyond  the  reach  of  man. 

(20)  My  mind  to  me  a  kingdom  is. 

(21)  No  admission  except  to  ticket  holders. 

(22)  Every  one  has  the  defects  of  his  qualities. 

(23)  Socrates  taught  that  no  man  would  knowingly 

do  wrong. 

(24)  And  silence,,  like  a  poultice,  comes  to  heal  the 

wounds  of  sound. 

(25)  All  the  world  admires  heroism. 

(26)  It  rains. 


CHAPTER    VI 
INDUCTION 

Generalization  and  What  it  Involves — In  the 
two  last  chapters  we  have  been  studying  the  use  of  lan- 
guage, the  most  important  instrument  of  thought.  We 
now  return  to  the  consideration  of  the  further  proc- 
esses mentioned  in  our  preliminary  survey  of  scientific 
method.  (Chap.  I.)  Observation  and  classification 
have  been  discussed  already ;  it  remains  to  examine  the 
way  in  which  laws  *  can  be  discovered  after  considerable 
body  of  facts  has  been  observed  and  classified.  We 
have  seen  that  a  law  is  a  statement  of  the  way  in  which 
facts  of  a  certain  kind  behave,  how  they  are  related  to 
other  facts,  what  are  the  universal  relations  in  which 
they  stand.  Our  first  question  is :  How  are  these  laws 
suggested?  What  is  the  source  of  these  general  state- 
ments of  relationship?  And  our  second  question  is: 
How  is  a  supposed  law  to  be  established  or  verified? 

In  answer  to  the  first  question,  it  may  be  said  that  a 
general  statement  is  usually  arrived  at  by  generalizing 
some  observed  relationship.  If  we  have  observed  one 
or  more  instances  in  which  a  cold  winter  has  been  fol- 
lowed by  a  hot  summer,  we  may  generalize  the  connec- 
tion and  assert  that  a  cold  winter  is  always  followed  by 
a  hot  summer,  that  there  is  an  invariable  and  inevitable 

i  The  previous  chapter  has  dealt,  in  part,  with. universal  propo- 
sitions; the  present  one  is  a  discussion  of  the  way  in  which  such 
propositions  are  established. 

79 


80  INDUCTION 

connection  between  them.  And  similarly  in  any  other 
case :  A  has  been  followed  by  B  and  we  conclude  that 
every  A  is  followed  by  B9  that  every  A  has  its  B.  A 
single  instance  may  be  enough  to  suggest  a  generaliza- 
tion. A  generalization  is  a  universal  assertion,  not  a 
mjore^attitude  of  expectation.  The  lower  animals  ex- 
hibit a  tendency  to  expect  a  given  thing  when  another, 
which  has  occurred  along  with  this,  reappears ;  when 
an  animal  hears  a  certain  call  he  may  expect  food,  be- 
cause in  the  past  the  two  have  been  connected;  when 
he  sees  a  blow  descending  he  may  expect  pain,  and  so 
on.  But  to  expect  a  thing  on  the  recurrence  of  another 
formerly  connected  with  it,  is  not  the  same  as  to  infer  a 
universal  connection.  When  I  perceive  A,  I  may  re- 
member and  expect  B,  without  ever  having  thought  of 
a  universal  relation  between  the  two,  without  asserting 
that  B  always  follows  A.  There  is  no  proof  that  an 
animal  can  generalize,  that  he  can  think  to  himself: 
"  A  call  of  a  certain  sort  is  followed  by  food,"  "  A 
blow  causes  pain,"  and  so  on.  He  hears  the  call  and 
expects  food,  but  he  does  not  generalize  the  connection. 
To  do  the  latter  would  be  difficult  if  not  impossible, 
without  language.  Tlais^power  to generalize,  to  iise_ 
general  and  abstract  ideas,  is  usually  regarded  as  one 
of  the  most  important  differences  between  human  and 
animal  intelligence. "" 

Without  generalization,  our  knowledge  would  be  con- 
fined to  individual  facts  or  to  groups  of  these.  We 
have  seen  that  knowledge  is  not  completed  by  the  mere 
accumulation  of  observations  and  the  classification  of 
what  has  been  observed.  The  aim  of  science  is  usually 
said  to  be  the  discovery  of  laws.  Now  a  law,  as  already 


LAWS  81 

remarked,  is  the  statement  of  the  way  in  which  phe- 
nomena behave,  or  the  way  in  which  they  are  inevitably 
related  to  other  phenomena. 

This  tendency  to  generalize  is,  then,  a  pre-condition 
of  all  but  the  most  primitive  kind  of  knowledge.  But, 
of  course,  our  generalization  may  not  turn  out  to  be  a 
law.  A  law  states  a  universal  connection  which  ac- 
tually holds  true,  whereas  our  hasty  generalization  may 
be  entirely  unsound.  A  generalization  arrived  at  in 
the  way  described  above  is  an  inductive  inference.  An 
inductive  inference  is  a  judgment  about  a  whole  class 
of  facts  based  upon  the  observation  of  individual  cases. 
It  is  a  universal  conclusion  based  upon  one  or  more 
particular  instances.  Obviously,  an  inductive  inference 
must  be  tested  or  verified;  but  before  proceeding  to  the 
discussion  of  verification  it  will  be  well  to  mention  cer- 
tain other  terms  which  are  frequently  employed  in  this 
connection. 

Causal  Connection. — The  terms,  cause,  causal  con- 
nection^ causal  law,  occur  constantly  in  this  part  of 
scientific  method.  What  is  a  cause?  The  term  implies 
a  connection  of  some  sort  between  phenomena;  but  of 
what  sort?  In  ordinary  usage  it  probably  means  most 
frequently  something  which  produces  or  brings  about 
something  else.  It  has  been  objected  that  we  can  never 
observe  one  thing  producing  another;  that  we  can  at 
most  observe  that  one  thing  is  followed  by  another,  and 
perhaps  find  reason  for  believing  that  it  will  always 
have  such  a  connection;  and  that  to  say  that  A  pro- 
duces B,  is  to  raise  a  metaphysical  question  with  which 
science  and  everyday  thinking  are  not  concerned.  But 
if  we  give  up  this  way  of  conceiving  cause,  what  can  we 


82  INDUCTION 

put  in  its  place  ?  Is  it  sufficient  to  say  that  cause  means 
simply  invariable  succession?  No,  for  the  succession  of 
day  and  night  is  an  invariable  succession.  The  notion 
of  cause  implies  that  the  relation  of  cause  and  effect 
not  only  is  invariable,  but  also  that  it  must  be  so  ;  that 
there  is  an  unconditional  or  necessary  -connection  be- 
tween the  two;  that  if  the  first  does  not  happen,  the 
second  cannot.  In  the  field  of  physical  phenomena,  it 
is  held  also  that  the  amount  of  energy  in  the  cause  is 
exactly  equal  to  the  amount  of  energy  in  the  sum-total 
of  its  effects;  in  other  words,  that  no  energy  is  either 
lost  or  created.  This  is  known  as  the  Law  of  the  Con- 
servation of  Energy.  Whether  it  applies  where  mental 
phenomena  are  concerned  has  been  questioned.  How- 
ever this  may  be,  cause  always  means  unconditional 
connection.2  Two  things  stand  in  a  relation  of  causal 
connection  when  they  are  so  related  that  one  is  the  un- 
conditional accompaniment  of  the  other  ;  the  cause  usu- 
ally occurs  or  begins  before  the  effect,  but  there  are 
cases  in  which  both  seem  to  begin  together.  Heat  is 
a  cause  of  expansion,  but  a  body  does  not  first  become 
hot  and  then  expand;  the  two  phenomena  occur  simul- 
taneously. A  causal  law  is  a  statement,  in  general 
terms,  of  a  causal  connection.  Thus  :  "  Heat  causes  ex- 
pansion." 

The  sort  of  generalization  which  is  most  frequently 
of  interest  and  importance  is  one  which  asserts  a  -con- 
nection of  this  sort,  although  this  is  not  the  only  sort 
which  may  be  investigated.  For  instance,  the  universal 


2  Of  course,  the  fact  that  a  connection  is  unconditional  cannot 
be  observed.  The  reasons  for  asserting  that  it  is  unconditional 
will  appetrrpresently. 


CO-EXISTENCE    AND    CAUSATION        83 

concurrence  of  two  properties  in  a  given  substance  may 
be  a  matter  of  importance,  but  their  connection  would 
not  be  called  a  causal  connection.  The  specific  gravity 
and  the  atomic  weight  of  carbon  would  be  a  case  in 
point.  The  co-existence  of  gravity  and  inertia  is  an- 
other example  mentioned  by  Bain ;  the  sciences  furnish 
innumerable  instances  of  a  like  sort.  Bain  remarks  that 
"  there  are  very  few  general  laws  of  pure  co-existence ; 
causation  is  singular  in  providing  a  comprehensive  uni- 
formity that  may  be  appealed  to  deductively  for  all 
cases.  The  uniformities  of  co-existence  (independent 
of  causation)  can  be  proved  only  piecemeal;  each  stands 
on  its  own  evidence  of  observation  in  detail;  no  one 
assists  us  to  prove  another."  The  causal  law  is  the  one 
to  which  we  shall  give  most  attention. 

Testing  Inductive  Inferences. — We  return  to  the 
question,  "  How  can  we  prove  an  inductive  inference  to 
be  true?  How  can  we  show  that  it  is  a  law?  "  There 
are  several  things  which  would  show  that  it  was  not 
true;  if  we  found  that  there  were  facts  which  were  in- 
consistent with  it,  or  if  it  were  found  to  be  inconsistent 
with  itself,  or  if  it  proved  to  be  in  disagreement  with 
any  established  law,  it  could  be  rejected  at  once.  But 
suppose  that  none  of  these  things  were  found ;  should 
the  inference  be  accepted  as  true?  Not  necessarily;  it 
might  be  that  our  observation  or  our  reflection  on  the 
case  had  been  insufficient  to  show  us  exceptions  or  in- 
consistencies if  such  did  exist.  If  we  have  inferred  a 
universal  connection  we  are  very  likely  to  overlook 
exceptions  or  to  forget  those  which  we  have  observed. 
A  good  many  people  still  believe  that  Friday  is  an  un- 
lucky day  and  that  the  number  13  brings  misfortune. 


84  INDUCTION 

But  even  if  no  exceptions  have  occurred  and  if  the  in- 
ference is  not  inconsistent  with  known  laws,  how  can 
we  be  assured  that  exceptions  may  not  occur  in  the 
future,  or  that  further  reflection  might  not  discover 
fatal  inconsistencies?  A  large  number  of  favorable 
cases  is  not  alone  sufficient  to  give  this  assurance.  The 
example  of  the  succession  of  day  and  night  illustrates 
that.  Millions  of  cases  do  not  prove  inevitable  con- 
nection. On  the  other  hand,  a  single  experiment  made 
.by  some  scientist  in  his  laboratory  may  be  sufficient  to 
establish  some  very  important  law.  "  Why,"  asks  Mill, 
"  is  a  single  instance  in  some  cases  sufficient  for  a  com- 
plete induction,  while  in  others  myriads  of  concurring 
instances,  without  a  single  exception  known  or  pre- 
sumed, go  such  a  very  little  way  towards  establishing 
an  universal  proposition?  Whoever  can  answer  this 
question  knows  more  of  the  philosophy  of  logic  than  the 
wisest  of  the  ancients,  and  has  solved  the  problem  of 
Induction."  Mill  himself  aided  very  materially  in  the 
formulation  of  the  conditions  under  which  we  do  regard 
our  inductive  inference  as  established,  and  the  inductive 
methods  presently  to  be  discussed  are  usually  called 
"  Mill's  methods."  Whether  or  not  he  has  solved  the 
whole  problem  of  induction  is  another  question  and  one 
with  which  we  shall  not  at  present  concern  ourselves. 

Complete  Enumeration. — There  are  -cases  in  which 
the  establishment  of  universal  conclusion  might  seem 
to  be  comparatively  easy.  It  is  sometimes  possible  that 
all  the  cases  of  a  given  sort  may  have  been  observed. 
For  example,  observation  has  shown  that  Mercury  re- 
volves about  the  sun ;  that  Venus  does  also ;  and  like- 
wise of  the  Earth,  Mars,  Jupiter  and  each  of  the  other 


COMPLETE    ENUMERATION  85 

planets.  We  can  say  then  with  perfect  safety,  that  all 
the  planets 3  revolve  about  the  sun.  The  universal 
statement  is  warranted  because  each  of  the  instances 
which  it  covers  has  been  observed.  We  are  saying  no 
more  in  the  conclusion  than  we  had  already  said  in  the 
several  statements  on  which  the  conclusion  is  based. 
The  universal  is,  in  fact,  simply  a  summary  way  of 
expressing  what  had  already  been  said.  It  is  merely  a 
"  telescoping  "  of  the  other  statements,  as  it  were.  This 
act  of  basing  a  general  statement  on  a  complete  enum- 
eration of  the  particular  cases  which  it  covers  has  been 
called  Perfect  Induction.  It  was  so  called  because  the 
conclusion  is  one  which  possesses  complete  certainty, 
whereas  most  inductive  inferences  are  more  or  less  un- 
certain. It  might  seem  then  that  this  was  the  solution 
of  the  problem  raised  above ;  you  are  sure  of  your  uni- 
versal if  you  have  seen  all  the  particulars  which  it 
covers.  But  how  can  we  be  sure  that  we  have  counted 
all  the  particulars?  The  field  of  observation  may  be 
so  small  and  so  easily  explored  that  every  existing  case 
may  be  observed.  But  even  if  all  existing  cases  have 
been  observed,  how  can  we  be  sure  that  others  may  not 
arise,  and  that  they  may  not  differ  from  those  we  have 
observed?  We  may  have  such  knowledge  about  a  class 
of  objects  as  will  enable  us  to  say  that  if  any  other 
members  of  the  class  should  come  into  existence  they 
would  be  like  those  already  known.  We  may  know 
that  the  sum  of  the  angles  of  every  plane  triangle 
which  may  ever  exist  will  be  equal  to  two  right  angles, 
not  because  we  have  counted  cases,  but  because  we  know 
that  this  necessarily  follows  from  the  properties  essen- 
s  Leaving  the  asteroids  out  of  consideration. 


86  INDUCTION 

tial  to  all  triangles.  However  numerous  the  class 
which  has  been  completely  observed,  the  knowledge 
that  each  of  the  observed  members  stands  in  certain 
relations  does  not  by  itself  assure  us  that  other  con- 
ceivable members  of  the  class  would  be  like  them  in  this 
respect.  Complete  enumeration  is  useful  as  an  abbre- 
viated way  of  stating  certain  kinds  of  information,  but 
it  throws  no  light  on  the  methods  of  discovering  uncon- 
ditional connections.4 

The  judgments  which  result  from  the  complete  enum- 
eration of  cases  have  been  called,  by  some  writers, 
Enumerative  Judgments  and  by  others,  Collective  Judg- 
ments. 

How  Generalizations  can  be  Verified — It  appears 
then  that  enumeration  of  all  the  existing  members  of 
a  class  does  not  enable  us  to  establish  laws.  Anything 
short  of  that  might  seem  to  leave  us  still  farther  from 
that  goal.  And  it  is  of  course  true,  as  appeared  on 
page  84,  that  an  incomplete  enumeration  of  instances 
furnishes  no  verification.  Then  if  verification  is  pos- 
sible at  all  it  can  not  rest  on  mere  enumeration,  or 
counting  of  cases.  Suppose  that  the  observation  of  one 


4  It  may  be  well  to  note  one  case  in  which  a  statement  in 
the  universal  form  must  be  distinguished  from  a  law.  As  an 
example,  we  may  take,  "  Every  three-sided  figure  is  a  triangle.'* 
This  is  not  an  inductive  inference;  it  is  not  based  upon  the  ob- 
servation of  individual  instances  at  all.  It  is  true  in  all  cases, 
but  it  is  true  because  we  have  previously  said,  "If  any  figure 
has  three  sides  we  will  call  it  a  triangle."  In  other  words,  it  is 
true  by  definition.  It  is  like  an  inductive  generalization  in  apply- 
ing to  all  possible  cases,  past,  present  and  to  come,  real  and 
imaginary,  etc.,  but  it  is  not  based  upon  the  observation  of  in- 
dividual facts.  Other  judgments  and  operations,  which  must  be 
distinguished  from  those  which  are  present  in  induction  properly 
so  called,  will  be  discussed  in  a  later  chapter;  and  still  others 
may  be  found  by  referring  to  Mill's  Logic,  Book  III,  chapter  ii. 


VERIFICATION  87 

or  more  instances  in  which  B  has  followed  A  has  sug- 
gested to  us  the  inference  that  A  and  B  are  causally 
related.  Let  us  ask  ourselves  what  consequences  would 
follow  upon  the  truth  of  this  inference.  In  the  first 
place  we  could  conclude  that  if  B  were  present  in  any 
case  A  must  have  been  present  also ;  and,  again,  if  A 
were  absent  in  any  case,  its  supposed  effect  B  must  have 
been  absent  also ;  or  if  either  A  or  B  varied  in  amount 
or  degree  the  other  should  show  a  corresponding  varia- 
tion. All  these  things  should  be  true  of  phenomena 
which  are  causally  related.  Phenomena  which  failed 
to  satisfy  such  conditions  could  not  be  unconditionally 
connected.  Suppose  we  had  inferred  that  absence  of 
oxygen  would  cause  death.  If  that  is  true,  an  animal 
immersed  in  nitrogen  should  die.  If  experiment  showed 
that  an  animal  could  live  under  such  conditions,  our 
inference  would,  of  course,  be  disproved ;  but  suppose 
the  animal  did  die,  would  the  inference  be  proved?  Not 
necessarily.  Perhaps  the  nitrogen  acted  as  a  poison 
or  perhaps  the  death  of  the  animal  was  due  to  rough 
handling,  etc.  Our  inductive  inference  would  be  com- 
pletely verified  only  if  we  could  show  that  death  could 
not  have  been  due  to  anything  except  the  absence  of 
oxygen.  If  we  could  be  sure  that  all  the  circumstances 
which  were  present  before  the  experiment  remained  pre- 
cisely the  same  with  the  one  exception  that  oxygen  was 
present  in  the  first  case  and  absent  in  the  second,  then 
we  should  have  shown  a  necessary  connection  between 
the  absence  of  oxygen  and  the  occurrence  of  death. 
Nothing  else  could  have  been  the  cause  because  all  were 
present  when  death  did  not  occur.  If  a  second  circum- 
stance were  present  when  the  phenomenon  occurred  and 


88  INDUCTION 

absent  when  it  did  not  occur,  it  would  dispute  with  the 
first  the  right  to  be  called  the  cause  and  no  final  con- 
clusion would  be  possible.  When  all  other  possibilities 
can  be  excluded,  the  one  which  remains  is  the  -cause. 
When  no  other  inference  is  consistent  with  the  facts, 
the  one  which  is  consistent  must  be  accepted  as  true. 

We  can  say,  then,  that  an  inductive  inference  is  com- 
pletely verified  when  we  have  found  facts  which  are  con- 
sistent with  its  truth  and  inconsistent  with  any  possible 
rival  inference;  or  more  briefly,  when  it  fits  the  facts 
and  no  alternative  inference  does.  We  establish  one  in- 
ference by  eliminating  all  others.  We  reason  that  the 
phenomenon  under  investigation  has  some  cause;  this 
other  phenomenon,  A,  may  be  the  cause;  it  fulfills  the 
requirements  and  no  other  does ;  therefore,  this  one  is 
and  must  be  the  cause  in  question.  There  are  several 
ways  of  selecting  or  grouping  instances  so  as  to  show 
that  some  one  factor  alone  satisfies  the  requirements. 
These  are  known  as  the  INDUCTIVE  METHODS. 

Observation,  and  Analysis  are  Presupposed. — One 
thing  should  not  be  forgotten.  It  is  that  the  application 
of  such  principles  as  these  presupposes  very  careful  ob- 
servation ;  if  we  are  to  be  certain  that  no  other  circum- 
stance is  present  when  a  given  phenomenon  is  present 
or  absent  when  it  is  absent,  we  must  have  observed  all 
the  other  circumstances.  In  ordinary  observation  we 
note  only  a  few  of  the  circumstances ;  if  we  are  un- 
trained observers  it  may  be  impossible  for  us  to  ob- 
serve more  than  a  few.  It  is  quite  impossible  for  a  child 
to  observe  in  a  flower  all  that  a  trained  botanist  can 
observe  there.  Accurate  observation  presupposes  anal- 
ysis, i.  e.t  breaking  up  the  total  complex  phenome- 


TEST    CONDITIONS  89 

non  into  its  element.  The  beginner  in  any  science  is 
unable  to  handle  the  facts  properly  because  he  is  un- 
able to  analyse  them;  he  sees  only  their  most  obvious 
characteristics. 

Postponing  Inference  till  Test  Conditions  are  Pres- 
ent— Before  we  begin  the  more  detailed  examination  of 
the  methods  of  verifying  an  inductive  inference,  there 
is  one  more  statement  to  be  made,  namely  this :  instead 
of  making  a  generalization  and  then  searching  for 
means  of  verifying  it,  we  may  refrain  from  drawing 
any  inference  until  we  have  before  us  a  group  of  facts 
which  will  make  it  possible  to  draw  a  correct  inference. 
In  other  words,  we  may  make  our  inference  under  test 
conditions.  Suppose,  for  example,  that  we  are  trying 
to  discover  the  cause  of  eclipses.  Before  making  any 
theories  on  the  subject  we  might  observe  a  number  of 
cases.  If  we  found  that  whenever  an  eclipse  occurred 
there  was  an  opaque  body  between  us  and  the  source 
of  light  and  that  at  other  times  everything  was  the 
same  except  that  there  was  no  body  in  that  position,  we 
should  infer  at  once  that  the  presence  of  the  opaque 
body  in  that  position  wa*s  the  cause  of  the  eclipse.  And 
so  in  any  other  case  we  might  form  no  theory  until  we 
had  facts  which  would  make  it  possible  to  form  a  cor- 
rect one. 

"  If  a  chemist  discovers  a  new  element,  he  will  pro- 
ceed to  try  a  variety  of  experiments  in  order  to  de- 
termine the  proportions  in  which  it  will  combine  with 
other  elements  as  well  as  to  discover  the  various  prop- 
erties of  such  combinations.  Supposing  such  experi- 
ments to  have  been  properly  conducted,  the  inductions 
at  which  he  arrives  will  be  perfectly  valid,  though  he 


90  INDUCTION 

may  have  formed  no  previous  theories  as  to  the  results 
of  his  researches.  Occasionally,  too,  an  induction  will 
not  be  the  result  of  any  definite  course  of  investigation, 
but  will  be  obtruded  on  our  notice."  5  But  such  cases  are 
rare,  and  ordinarily  we  have  some  theory  before  we  have 
the  facts  which  will  verify  it. 

It  is  often  better  to  draw  an  inference  early  in  the 
investigation ;  the  reasons  for  this  will  be  discussed  in 
a  later  chapter.6  In  the  meantime  it  should  be  remem- 
bered that  the  Inductive  Methods  which  are  now  to  be 
discussed  may  be  used  either  to  test  an  inference  al- 
ready made  or  to  furnish  a  basis  for  drawing  a  correct 
inference  if  none  has  previously  been  drawn. 

The  Inductive  Methods. — I.  AGREEMENT.  Sup- 
pose we  find  that  A  was  followed  by  B  in  a  number  of 
instances,  but  that  the  attendant  circumstances  varied 
greatly.  Suppose,  for  example,  that  three  or  four  in- 
dividuals, of  different  races,  different  habits  of  life, 
and  otherwise  as  different  as  possible,  were  all  bitten 
by  a  certain  kind  of  mosquito  and  that  each  developed 
yellow  fever:  would  not  such  a  set  of  cases  give  some 
warrant  to  the  inference  that  \he  bite  of  the  mosquito 
was  causally  connected  with  the  development  of  the 
fever?  The  fact  that  these  individuals  were  different 
in  all  other  respects  would  seem  to  exclude  the  possi- 
bility that  anything  else  could  have  been  the  cause. 

Or  suppose  again  that  we  find  dew  deposited  on  two 
or  more  objects  which  differ  in  position,  chemical  com- 
position, character  of  surface,  and,  in  short,  all  respects 
except  that  both  are  cooler  than  the  surrounding  atmo- 

B  Fowler,  Inductive  Logic,  p.  11. 
«  Part  III,  chapter  ii,  Hypothesis. 


THE    METHOD    OF    AGREEMENT         91 

sphere ;  we  should  have  good  grounds  for  believing  that 
this  last  characteristic  was  causally  related  to  the  dep- 
osition of  dew. 

Or,  once  more,  if  a  number  of  persons  who  recovered 
from  a  given  disease  were  similar  only  in  having  used 
a  certain  drug,  the  inference  would  be  that  the  drug 
was  causally  related  to  the  cure. 

In  each  of  these  examples  we  have  a  set  of  instances 
in  which  a  given  phenomenon  is  present,  an  attack  of 
fever,  deposition  of  dew,  recovery  from  illness ;  nothing 
else  is  present  in  all  cases  except  one  other  phenomenon, 
being  bitten  by  the  mosquito,  being  cooler  than  the 
surrounding  air,  having  used  a  certain  drug.  Our  infer- 
ence is  that  the  phenomena  which  are  constantly  pres- 
ent together  are  causally  related.  If  A  is  causally,  i.  e.9 
unconditionally,  related  to  something  else,  that  thing 
must  be  present  when  A  is  present.  As  only  one  other 
phenomenon  is  present  in  all  cases,  that  alone  among 
all  those  at  any  time  present  can  be  causally  related 
to  the  first.  This  method  of  isolating  the  phenomena 
which  are  so  related  is  known  as  the  Method  of  Agree- 
ment. Mill's  statement  of  the  Canon  of  Agreement  is 
as  follows :  "  If  two  or  more  instances  of  the  phenom- 
enon under  investigation"  [fever,  deposition  of  dew, 
etc.],  "  have  only  one  circumstance  in  common  "  [being 
bitten  by  a  mosquito,  being  cooler  than  the  surrounding 
air,  etc.  ] ,  "  the  circumstances  in  which  alone  all  the  in- 
stances agree  is  the  cause  (or  effect)  of  the  given  phe- 
nomenon." His  statement  of  the  axiom  of  this  method 
is :  "  Whatever  circumstance  can  be  excluded  without 
prejudice  to  the  phenomenon,  or  can  be  absent  notwith- 
standing its  presence,  is  not  connected  with  it  in  the  way 


92  INDUCTION 

of  causation."  The  only  circumstance  which  is  com- 
mon to  a  number  of  instances  in  which  a  given  phe- 
nomenon is  present,  is  causally  related  to  it,  because  all 
the  rest  are  excluded  by  the  fact  that  they  are  separable 
from  it. 

In  this  method,  as  in  the  others  to  be  discussed, 
the  point  of  first  importance  is  that  we  are  selecting 
instances  of  the  occurrence  of  a  phenomenon,  and 
selecting  them  in  such  a  way  as  to  identify  the  cir- 
cumstance or  circumstances  causally  related  to  the 
phenomenon.  We  might  re-word  the  main  points  as 
follows:  select  instances  in  which  the  phenomenon  under 
investigation  is  present,  but  which  are  as  different  as 
possible  in  all  other  respects ;  if  there  is  one  circum- 
stance and  one  only  which  is  always  present  when  the 
phenomenon  under  investigation  is  present,  that  cir- 
cumstance is  causally  related  to  the  phenomenon. 

Difficulties  in  Using  this  Method. — An  ideal  case 
might  be  represented  symbolically  in  this  way:  let  the 
phenomenon  under  investigation  be  represented  by  x; 
and  let  the  accompanying  circumstances,  in  the  severaJ. 
instances  we  have  selected  be  represented  by  abcde* 
afghi,  ajklm,  respectively ;  or  the  phenomenon  and  its 
accompanying  circumstances  by : 

abcdex 
a-fgliix 
ajklmx. 

The  only  circumstances  common  to  all  the  instances  is 
a.     Therefore  a  is  causally  related  to  x.     No  actual 


DIFFICULTIES  93 

case  would  be  quite  so  simple ;  any  phenomenon  has 
among  its  accompanying  circumstances  everything  that 
is  happening  in  the  universe  at  the  time  of  its  occur- 
rence. Most  of  these  circumstances  can,  of  -course,  be 
eliminated  as  irrelevant ;  still  it  is  easily  possible  to 
overlook  something  that  is  relevant. 

1.  Circumstances  which  might  seem  to  have  no  con- 
nection with  the  phenomenon  may  be  causally  related 
to   it.     For  example,   it  might  be  supposed  that  the 
number  of  sun-spots  had  no  relation  to  financial  con- 
ditions ;  yet  it  has  been  shown  that  the  periods  when 
sun-spots  are  most  numerous  have  the  same  frequency 
as  the  periods  when  panics  occur ;  and  it  has  been  sug- 
gested that  sun-spots  influence  climatic  conditions,  that 
these  in  turn,  by  influencing  crops,  and  so  on,  do  affect 
financial  conditions.    Whether  there  is  any  truth  in  this 
or  not,  it  will  remind  us  that  it  is  not  easy  to  determine 
just  what  circumstances  are  relevant. 

2.  Another  difficulty  arises  from  the  fact  that  analy- 
sis is  never  complete;  not  all  the  elements  are  singled 
out,  and  some  of  those  which  have  been  overlooked  may 
be  all-important.   For  example :  it  had  been  noticed  that 
persons  who  had  been  much  out  of  doors  at  night  were 
more  likely  than  others  to  be  attacked  by  malaria;  it 
was  inferred  that  "  night-air  "  was  a  cause  of  malaria, 
and  consequently  people  tried  to  exclude  it  from  their 
houses.    Later  it  was  shown  that  the  attacks  of  mos- 
quitoes were  the  causes.   Mosquitoes  are  more  active  at 
night,  but  instead  of  noting  this,  the  more  obvious  fact 
that  "  night-air  "  is  damp,  and  so  on,  was  selected  as 
the  important  one.     When  it  was  found  that  the  bite 


94  INDUCTION 

of  the  mosquito  was  the  circumstance  always  present, 
while  the  time  of  the  attack  made  no  difference,  the 
older  theory  was  overthrown. 

In  symbolizing  an  actual  case  we  should  need  some- 
thing to  represent  the  circumstances  which  were  dis- 
regarded or  overlooked.  We  might  use  the  symbol 
X;  the  accompanying  circumstances  would  then  be  rep- 
resented by  abode.  .X9  afghi.  .X,  etc.  This  would  in- 
dicate that  there  is  a  margin  of  uncertainty  in  such 
cases. 

3.  There  is  one  other  difficulty  in  the  application  of 
the  method  of  Agreement.  It  may  be  illustrated  in  this 
way :  suppose  a  man  should  drink  coffee  with  his  lunch- 
eon on  one  day  and  afterwards  smoke  a  strong  cigar; 
suppose  on  the  following  day,  with  a  different  bill  of 
fare,  he  should  drink  tea  and  smoke  a  cigar;  on  both 
days  he  has  a  headache  in  the  afternoon.  The  applica- 
tion of  the  method  of  Agreement  would  lead  him  to  be- 
lieve that  the  cigar  was  the  -cause  of  the  headache,, 
whereas  the  cause  may  have  been  the  coffee  in  one  in- 
stance and  the  tea  in  the  other.  This  illustrates  what 
is  known  as  the  Plurality  of  Causes.  A  given  phenome- 
non may  have  one  cause  in  one  instance  and  another 
cause  in  a  second  instance.  It  is  sometimes  said  that  if 
our  analysis  were  complete  we  should  find  that  a  given 
phenomenon  always  had  the  same  cause ;  that  in  the  in- 
stances just  mentioned,  the  cause  of  the  headache  wag 
something  common  to  tea  and  coffee ;  or  that  the  head- 
ache caused  by  coffee  differs  from  that  caused  by  tea 
and  that  two  things  which  are  different  never  can  pro- 
duce the  same  effect.  Perhaps  that  is  true,  but  the  fact 
still  remains  that,  in  practice,  effects  which  are  so  simi- 


THE    METHOD    OF    DIFFERENCE         95 

lar  as  to  be  indistinguishable  may  be  produced  by  causes 
that,  for  ordinary  observation,  are  very  different.  This 
makes  a  very  serious  limitation  to  the  application  of 
the  method  of  Agreement.  The  method  is  still  valuable 
as  suggesting  causal  relations,  though  imperfect  as  a 
means  of  proof.  May  it  not  be  possible  to  select  in- 
stances on  some  other  principle  in  such  a  way  as  to 
obviate  some  of  these  difficulties? 

II.  THE  METHOD  OF  DIFFERENCE. — Take  another 
concrete  case :  suppose  two  individuals  as  similar  as 
possible  in  all  respects,  race,  family,  occupation,  man- 
ner of  living,  state  of  health  and  so  on;  one  of  these 
is  bitten  by  mosquitos  of  a  certain  sort  and  the  other 
protects  himself  against  their  attacks ;  the  first  con- 
tracts the  fever,  the  second  escapes  it.  We  should 
regard  such  a  group  of  facts  as  warranting  the  conclu- 
sion that  the  bite  of  the  mosquito  and  the  contraction 
of  yellow  fever  were  causally  related. 

Or,  if  two  objects  of  similar  chemical  construction, 
character  of  surface,  location,  etc.,  differed  only  in  that 
one  was  for  some  reason  cooler  than  the  surrounding 
air,  while  the  other  was  not,  and  if  dew  were  deposited 
on  the  first  and  not  on  the  second,  we  should  conclude 
that  the  cooler  temperature  of  the  one  was  causally 
related  to  the  deposition  of  dew  upon  it.  , 

Cases  like  these  illustrate  the  Method  of  Difference." 
Mill's  statment  of  the  Canon  of  this  method  is : 

"  If  an  instance  in  which  the  phenomenon  under  in- 
vestigation occurs,  and  an  instance  in  which  it  does  not 
occur,  have  every  circumstance  in  common  save  one, 
that  one  occurring  only  in  the  former;  the  circum- 
stance in  which  alone  the  two  instances  differ  is  the 


96  INDUCTION 

effect  or  the  cause,  or  an  indispensable  part  of  the 
cause,  of  the  phenomenon."  Its  axioms,  in  the  words 
of  the  same  writer,  are :  "  Whatever  antecedent  cannot  be 
excluded  without  preventing  the  phenomenon,  is  the 
cause,  or  a  condition  of  the  phenomenon;  whatever  con- 
sequent can  be  excluded  with  no  other  difference  in  the 
antecedents  than  the  exclusion  of  a  particular  one,  is 
the  effect  of  that  one." 

Relation  of  this  to  the  First  Method. — We  quote 
from  Mill  again  regarding  the  relation  of  this  method 
to  the  other: 

"  Instead  of  comparing  different  instances  of  a  phe- 
nomenon to  discover  in  what  they  agree,  this  method 
compares  an  instance  of  its  occurrence  with  an  instance 
of  its  non-occurrence,  to  discover  in  what  they  differ. 
.  .  .  Both  are  methods  of  elimination.  ...  The 
Method  of  Agreement  stands  on  the  ground  that  what- 
ever can  be  eliminated  is  not  connected  with  the  phe- 
nomenon by  any  law.  The  Method  of  Difference  has 
for  its  foundation,  that  whatever  cannot  be  eliminated 
is  connected  with  the  phenomenon  by  a  law." 

Incomplete  analysis  of  the  circumstances  attending 
the  phenomenon  may  vitiate  the  inference  in  both 
methods:  in  the  method  of  Agreement  as  already 
stated;  in  the  method  of  Difference,  by  leading  us  to 
overlook  points  of  difference  in  cases  supposed  to  be 
alike  except  in  the  particulars  specified  in  the  Canon 
of  this  method. 

Difficulties  in  Using  the  Method  of  Difference. — 1. 
One  danger  in  employing  the  method  of  Difference 
results  from  the  possibility  of  the  Composition  of 
Causes.  It  often  happens  that  a  given  phenomenon 


DIFFICULTIES  97 

is  the  effect  of  the  joint  action  of  several  causes.  Heat, 
light,  moisture,  etc.,  are  all  causally  related  to  the  life 
of  plants.  If  two  plants  were  similarly  situated  as 
regards  all  but  moisture,  it  would  be  incorrect  to  con- 
clude that  moisture  was  the  sole  cause  of  the  life  of 
the  one  because  its  absence  was  followed  by  the  death 
of  the  other.  Application  of  the  method  of  Difference 
does  show  that  the  antecedent  is  causally  related  to  the 
consequent,  but  not  that  it  is  the  sole  or  adequate  cause. 

If  we  could  supplement  the  method  of  Difference  by 
the  method  of  Agreement,  if  we  could  find  a  set  of  in- 
stances in  which  the  supposed  cause  was  alone  common 
to  the  cases  in  which  the  phenomenon  was  present,  then 
we  could  conclude  that  this  supposed  cause  was  ade- 
quate to  produce  the  phenomenon. 

£.  Another  source  of  difficulty  closely  connected  with 
the  one  just  discussed  is  to  be  found  in  the  existence  of 
Counteracting  Causes.  Even  if  a  cause  is  adequate  to 
the  production  of  an  effect  under  ordinary  conditions, 
it  may  fail  to  produce  it  owing  to  the  presence  of  some 
opposed  tendency.  The  poison  can  be  counteracted  by 
an  antidote ;  the  tendency  of  the  moon  to  fall  to  the 
earth  is  in  part  overcome  by  centrifugal  force,  and  so 
on.  The  presence  of  a  counteracting  cause  might  lead 
us  to  overlook  the  real  cause  of  the  phenomenon.  The 
cause  is  present  without  the  effect;  that  is,  without  the 
usual  effect.  In  such  a  case  its  effect  is  to  be  found  in 
its  modification  of  the  counteracting  cause.  The  ten- 
dency of  the  moon  to  fall  does  modify  the  effect  which 
would  otherwise  be  produced  by  its  tendency  to  fly  off  at 
a  tangent.  We  may  symbolize  one  sort  of  case  in  which 
error  might  arise,  as  follows :  Let  m  be  the  phenomenon 


98  INDUCTION 

whose  cause  we  are  seeking  and  suppose  that  we  have 

abed  X 
abcr  X  m 

We  should  probably  conclude  that  r  was  the  cause  of 
m,  whereas  it  might  well  be  that  a  was  the  real  cause,  but 
that  it  was  counteracted  in  the  first  instance  by  d.  It 
is  no  doubt  true  that  in  an  ideal  application  of  the 
methods  there  would  be  little  difficulty ;  if  we  could  get 
cases  which  differed  in  only  one  circumstance  it  would 
at  any  rate  be  easy  to  see  that  the  absence  of  the  effect 
m  was  connected  with  the  presence  of  the  circumstance 
d;  we  should  still  have  to  search  for  the  cause  of  m's 
presence.  But  in  actual  cases  the  matter  is  not  so  sim- 
ple; we  cannot  find  ideal  cases  and  the  instances  we 
select  for  the  application  of  the  method  of  Difference 
may  differ  in  more  than  one  respect,  as  in  the  case  just 
discussed. 

III.  THE  JOINT  METHOD. — Nature  presents  very 
few  instances  in  which  the  method  of  Difference  can  be 
directly  applied,  and  even  experiment  fails  to  present 
ideal  conditions.  It  seldom  happens  that  the  conditions 
stated  in  the  Canon  of  Difference  are  realized.  The 
same  is  true  to  a  great  extent  with  regard  to  the  method 
of  Agreement.  Usually  two  or  more  cases  in  which  a 
given  phenomenon  occurs  are  similar  in  more  than  one 
circumstance.  In  such  cases  it  is  sometimes  possible  to 
use  a  combination  of  the  two  methods.  The  following 
instance  illustrates  the  use  of  The  Joint  Method  of 
Agreement  and  Difference:  a  large  number  of  cases  of 
typhoid  fever  occurred  at  about  the  same  time  in  a 
college  community.  It  happened  that  all  those  who  de- 


THE    JOINT    METHOD  99 

veloped  the  disease  ate  at  a  certain  few  fraternity  and 
boarding-house  tables.  The  water  supply  was  first  in- 
vestigated. It  was  found  that  all  these  places  used 
water  from  the  same  source.  But  it  was  also  true  that 
the  other  houses  were  supplied  from  the  same  source, 
so  this  possible  cause  was  eliminated.  The  fresh  vege- 
tables were  supplied  from  various  sources;  some  of  the 
places  in  which  the  disease  was  developed  used  one 
;  source,  others  a  different  one ;  moreover,  the  places  in 
which  the  disease  was  not  developed  were  supplied  from 
the  same  variety  of  sources.  The  other  food  supplies 
fcame  from  various  places  and  the  method  of  Agreement 
ncould  not  be  applied  so  far  as  they  were  concerned,  with 
cone  exception ;  it  appeared  that  the  milk  supply  was  the 
same  for  all  the  places  in  which  the  fever  was  developed, 
whereas  none  of  the  places  which  escaped  used  milk 
from  that  source.  The  inference  was  that  the  milk 
contained  the  cause  of  the  disease.  Further,  it  was 
found  that  when  milk  from  this  source  was  no  longer 
used,  no  new  cases  of  the  disease  appeared.  There  were 
two  sets  of  cases:  in  one  the  disease  was  developed,  in 
the  other  it  was  not.  Those  in  which  it  appeared  were 
alike  in  several  respects ;  the  ages,  habits  and  previous 
general  health  were  similar  in  all ;  the  water  supply  was 
the  same  and  also  the  milk  supply ;  it  might  be  any  one 
of  these;  the  method  of  Agreement  could  not  be  suc- 
cessfully applied.  The  other  set  of  cases,  those  in  which 
the  disease  did  not  appear,  were  like  the  first  in  many 
respects,  but  there  was  no  one  of  these  which  differed 
from  any  one  of  the  others,  in  one  respect  only.  There 
was  one  and  one  only  circumstance  in  which  all  the 
members  of  the  first  group  differed  from  all  the  mem~ 


100  INDUCTION 

bers  of  the  second,  namely  in  the  milk  supply.  All  of 
one  group  agreed  in  having  a  given  milk  supply  and 
developing  typhoid  fever;  all  of  the  other  group 
agreed  in  using  milk  from  another  source  and  escaping 
the  disease.  Comparing  group  with  group  the  method 
of  Difference  could  be  used.  There  was  only  one  cir- 
cumstance in  which  all  the  instances  in  which  fever  was 
developed  differed  from  all  of  those  in  which  it  was  not 
developed.  Within  each  set  of  instances  there  is  a 
partial  application  of  the  method  of  Agreement.  One 
set  agreed  in  having  the  disease  and  also  in  having  an- 
other common  circumstance ;  but  more  than  one  circum- 
stance was  common,  so  the  application  could  not  be 
complete;  similarly  the  other  set  of  instances  agreed 
in  the  absence  of  the  fever  and  in  the  absence  of  this 
circumstance;  but  they  also  agreed  in  lacking  va- 
rious other  circumstances.  However,  they  agreed 
in  lacking  only  one  which  was  present  in  all  those 
of  the  other  set,  and  that  is  the  important 
point. 

The  two  sets  of  instances  might  be  symbolized  thus ; 
p  representing  the  phenomenon  under  investigation: 

abcdr  X  p  bcJcr 

abefr  X  p  eflr 

aefgr  X  p  fgmr 

afghrX  p  ghnr 

Both  a  and  r  are  common  to  all  the  instances  in  which  p 
is  present,  but  r  is  excluded  by  the  fact  that  it  is  pres- 
ent in  those  in  which  p  is  absent. 

Mill's  statement  of  the  Canon  of  the  Joint  Method 
reads :     "  If  two  or  more  instances  in  which  the  phe- 


THE    JOINT    METHOD,.    .  101 

nomenon  occurs  have  only  one  circumstance  iji  com- 
mon, while  two  or  more  instances  in  .wMrii  it  du«?s;  r«;o]fc, 
occur  have  nothing  in  common  save  the  absence  of  that 
circumstance,  the  -circumstance  in  which  alone  the  two 
sets  of  instances  differ  is  the  effect  or  the  cause,  or  an 
indispensable  part  of  the  cause,  of  the  phenomenon." 
This  statement  does  not  quite  cover  a  case  like  that 
described  above.  The  instances  in  which  the  phenome- 
non occurs  may  have  more  than  one  circumstance  in 
common,  provided  that  there  is  only  one  which  is  at  the 
same  time  common  to  these  and  absent  from  those  in 
which  the  phenomenon  does  not  occur.  We  might  re- 
state it  thus :  "  If  two  or  more  instances  in  which  a 
phenomenon  occurs  have  in  common  one  circumstance 
which  is  at  the  same  time  the  only  circumstance  present 
in  these  instances  and  absent  from  two  or  more  instances 
in  which  the  phenomenon  does  not  occur,  that  circum- 
stance is  causally  related  to  the  phenomenon."  This 
form  of  statement  avoids  the  difficulty  just  mentioned 
and  also  another.  It  is  practically  impossible  to  find 
a  set  of  instances  which  have  nothing  in  common  save 
the  absence  of  one  circumstance.  In  the  example  just 
given,  the  instances  in  which  typhoid  fever  did  not  oc- 
cur agreed  in  not  being  Esquimaux  nor  octogenarians 
nor  coal-miners,  and  so  on  indefinitely.  On  the  other 
hand  it  would  have  been  easily  possible  to  find  a  group 
of  instances  in  which  there  would  have  been  fewer  cir- 
cumstances absent  from  all.  One  might  select  a  num- 
ber of  individuals  from  different  races,  of  different  ages, 
occupations,  and  so  on.  Fewer  circumstances  would  be 
absent  from  all  of  these  than  from  a  homogeneous  group 
of  college  students.  But  such  instances  might  be  en- 


102  INDUCTION 

tirely  insignificant  fW  the  purpose  of  discovering  the 
••C'l-usr.  of  tlte  "disease.'  --Of  course,  if  the  group  of  nega- 
tive instances  included  examples  from  all  varieties  of 
those  who  lacked  the  phenomenon  in  question,  and  we 
could  discover  the  only  circumstance  lacking  in  these, 
and  present  in  the  cases  where  the  phenomenon  was 
present,  a  conclusion  could  be  drawn;  but,  in  the  first 
place,  it  would  be  impossible  to  get  such  a  group,  for 
it  would  be  infinite  in  extent ;  and,  secondly,  if  the  group 
i  could  be  had,  the  discovery  of  the  only  circumstance 
"lacking  from  all  of  them  would  be  an  endless  task.  Most 
i  of  such  instances  might  at  once  be  eliminated  as  irrele- 
vant, though  Mill's  canon  does  not  provide  for  that. 
.It  is  important  that  the  instances  in  which  the  phe- 
-nomenon  is  absent  should  be  similar  to  those  in  which 
:'it  is  present,  for  if  there  are  many  points  of  difference 
•Jit  will  be  difficult  or  impossible  to  select  those  which  are 
causally  related  to  the  phenomenon. 

IV.  CONCOMITANT  VARIATIONS. — There  are  still 
otlier  methods  of  discovering  causal  relations.  Suppose 
a  case  in  which  such  instances  as  are  demanded  for  the 
application  of  any  of  the  foregoing  methods  cannot  be 
obtained;  it  may  be  possible  to  find  instances  in  which 
the  phenomenon  occurs  in  varying  degrees  or  in  dif- 
ferent quantities,  while  some  other  phenomenon  varies 
concomitantly.  "  The  effects  of  heat  are  known  only 
through  proportionate  variation.  We  can  not  deprive 
a  body  of  all  its  heat ;  the  nature  of  the  agency  forbids 
us.  But  by  making  changes  in  the  amount,  we  ascer- 
tain concomitant  changes  in  the  accompanying  cir- 
cumstances, and  can  so  establish  cause  and  effect.  It  is 
thus  that  we  arrive  at  the  law  of  the  expansion  of  bodies 
by  heat.  In  the  same  way  we  prove  the  equivalence  of 


CONCOMITANT    VARIATIONS  103 

heat  and  mechanical  force  as  a  branch  of  the  great 
law  of  Conservation  of  Persistence  of  Force." 

"  The  proof  of  the  First  Law  of  Motion,  as  given 
by  Newton,  assumed  the  form  of  Concomitant  Varia- 
tions. On  the  earth,  there  is  no  instance  of  motion 
persisting  indefinitely.  In  proportion,  however,  as  the 
known  obstructions  to  motion — friction  and  the  resist- 
ance of  the  air — are  abated,  the  motion  of  a  body  is 
prolonged.  A  wheel  spinning  in  an  exhausted  receiver 
upon  a  smooth  axle  runs  a  very  long  time.  In  Borda's 
experiment  with  the  pendulum,  the  swing  was  prolonged 
to  more  than  thirty'  hours,  by  diminishing  the  friction 
and  exhausting  the  air.  Now,  comparing  the  whole 
series  of  cases,  from  speedy  exhaustion  of  movement  to 
prolonged  continuance,  we  find  that  there  is  a  strict 
concomitance  between  the  degree  of  obstruction  and  the 
arrest ;  we  hence  infer  that  if  the  obstruction  were  en- 
tirely absent,  motion  would  be  perpetual.  The  statis- 
tics of  crime  reveal  causes  by  the  method  of  Variations. 
When  we  find  crimes  diminishing  according  as  labor  is 
abundant,  according  as  habits  of  sobriety  have  in- 
creased, according  to  the  multiplication  of  the  means  of 
detection,  or  according  to  the  system  of  punishments, 
we  may  presume  a  causal  connection,  in  circumstances 
not  admitting  of  the  method  of  Difference."  7 

We  may  symbolize  a  Set  of  instances  to  which  this 
method  is  applicable  in  this  way: 

a  bed  X  p 
!(2fl)  bee  X  (2p) 
(4a)  bef  X  (3p),  etc. 

The  Canon  of  the  Method  of  Concomitant  Variations 
7  Bain,  Logic,  pp.  62-63. 


104  INDUCTION 

is :  "  Whatever  phenomenon  varies  in  any  manner 
whenever  another  phenomenon  varies  in  some  particular 
manner,  is  either  a  cause  or  an  effect  of  that  phenome- 
non, or  is  connected  with  it  through  some  fact  of  cau- 
sation." 

V.  THE  METHOD  OF  RESIDUES.  This  method  is 
usually  included  with  the  others  and  completes  the  list. 
Its  canon  is :  "  Subduct  from  any  phenomenon  such 
part  as  is  known  by  previous  inductions  to  be  the  effect 
of  certain  antecedents,  and  the  residue  of  the  phenom- 
enon is  the  effect  of  the  remaining  antecedents."  Its 
principle,  like  that  of  the  other  methods,  is  that  of  ex- 
clusion. If  we  have  a  complex  phenomenon  or  a  group 
of  phenomena  represented  by  the  letters  xyzlm,  and  a 
group  of  antecedent  circumstances  represented  by 
abcdf,  and  if  we  know  that  a  causes  x  and  b  causes  «/,  c 
causes  z  and  d  causes  Z,  the  conclusion  will  be  that  the 
remaining  m  is  the  effect  of  /.  This  method  would  be 
equally  applicable  in  an  instance  in  which  the  causes 
were  present  with  the  effects  instead  of  being  ante- 
cedent to  them  only.  Thus,  if  we  had  a  phenomenon 
m  in  a  group  of  circumstances,  dbcdjxyzlm,  and  knew 
as  before  that  a  and  #,  b  and  y,  c  and  z,  and  d  and  I 
were  causally  related,  the  connection  of  /  and  m  would 
be  evident.  We  must,  of  course,  be  careful  to  include 
all  the  relevant  circumstances  in  the  group. 

If  a  phenomenon  has  occurred  and  all  the  known  ante- 
cedents of  this  phenomenon  are  known  not  to  contain 
its  cause,  the  cause  must  be  sought  for  in  some  phe- 
nomenon not  yet  discovered.  There  were  certain  per- 
turbations in  the  movement  of  the  planet  Uranus,  not 
accounted  for  bjr  the  attractive  force  of  any  known 


THE    METHOD    OF    RESIDUES          105 

heavenly  body;  they  must,  then,  be  due  to  some  body 
not  yet  discovered ;  this  line  of  reasoning  led  to  the  dis- 
covery of  the  planet  Neptune. 

Again,  the  weight  of  atmospheric  nitrogen  was 
found  to  be  greater  than  that  of  nitrogen  produced 
chemically ;  further  examination  revealed  the  presence 
in  the  atmosphere  of  another  element,  argon. 

Obviously  the  method  of  Residues  can  be  applied 
only  when  we  have  fairly  complete  knowledge  of  the 
field  of  facts  in  which  the  phenomenon  is  found.  We 
must  know  the  causal  relations  of  all  the  circumstances 
involved  in  the  case  except  the  phenomenon  under  inves- 
tigation. 

The  following  example,  though  not  formally  in- 
cluded under  Mill's  canon,  employs  the  principle  of 
Residues :  If  only  four  men  were  capable  of  doing  a  cer- 
tain act  and  if  we  learned  that  one  of  these  was  tempo- 
rarily unable  to  do  it,  through  illness,  and  that  the  two 
others  were  a  thousand  miles  away  when  the  act  was 
performed,  the  fourth  must  have  committed  the  act. 

If,  in  any  way,  we  can  assure  ourselves  that  of  all  the 
possible  causes  of  a  phenomenon  all  but  one  are  ex- 
cluded, that  one  must  be  the  cause.  The  several  methods 
are  ways  of  doing  this. 

EXERCISES 

Examine  the  following  arguments  and  criticise  the  rea- 
soning as  fully  as  possible;  state  the  method  used: 

1.  The  newly  discovered  painting  must  be  a  Rubens; 
for  the  conception,  the  drawing,  the  tone  and  the  tints  are 
precisely  those  seen  in  the  authentic  works  of  that  master. 
(Hyslop.) 


106 


INDUCTION 


2.  In  nine  counties,  in  which  the  population  is  from  100 
to  150  per  square  mile,  the  births  to  100  marriages  are  396; 
in  sixteen  counties,  with  a  population  of   150  to  200  per 
square  mile,  the  births  are  390  to  100  marriages.     There- 
fore the  number  of  births  per  marriage  is  inversely  related 
to    the    density    of    population    and    contradicts  Malthus's 
theory  of  the  law  of  population.      (Hyslop.) 

3.  The  great  famine  in  Ireland  began  in  1845  and  in- 
creased  until  it  reached   a   climax   in    1848.     During  this 
time  agrarian  crime  increased  very  rapidly  until,  in  1848, 
it  was  more  than  three  times  as  great  as  in  1845.     After 
this  it  decreased  with  the  return  of  better  crops  until,  in 
1851,  it  was  only  50  per  cent,  more  than  in  1845.      It  is 
evident  from  this  that  a  close  relation  of  cause  and  effect 
exists  between  famine  and  agrarian  crime.      (Hyslop.) 

4.  The  influence  of  heat  in  changing  the  level  of  the 
ground  upon  which  the  temple  of  Jupiter  Serapis  stands 
might  be  inferred  from  several  circumstances.     In  the  first 
place,  there  are  numerous  hot  springs  in  the  vicinity,  and 
when  we  reflect  on  the  dates  of  the  principal  oscillations  of 
level  this  conclusion  is  made  much  more  probable.     Thus, 
before  the  Christian  era,  when  Vesuvius  was  regarded  as  a 
spent  volcano,  the  ground  on  which  the  temple  stood  was 
several  feet  above  water.     But  after  the  eruption  of  Vesu- 
vius  in   79   B.   c.,   the  temple  was   sinking.     Subsequently 
Vesuvius  became  dormant  and  the  foundations  of  the  tem- 
ple began  to  rise.     Again  Vesuvius  became  active,  and  has 
remained  so  ever  since.     During  this  time  the  temple  has 
been    subsiding    again,    so    far    as    we    know    its    history. 
(Hyslop.) 

5.  Take  a  bottle  of  charged  water,  slightly  warmer  than 
a  given  temperature  registered  by  the  thermopile,  and  mark 
the  deflection  it  causes.      Then  cut  the  string  which  holds  it 
and  the  cork  will  be  driven  out  by  the  elastic  force  of  the 
carbonic  acid  gas.     The  gas  performs  its  work,  and  in  so 
doing  it  consumes  heat  and  the  deflection  of  the  thermopile 
shows  that  the  bottle  is  cooler  than  before,  heat  having 
been  lost  in  the  process.      (Hyslop.) 

6.  As   an   evidence  of  the  extreme   antiquity  of  highly 
civilized  man,  we  have  the  following  facts :      On  one  of  the 
remote  islands  of  the  Pacific — Easter  Island — two  thousand 


EXERCISES  107 

miles  from  South  America,  two  thousand  miles  from  the' 
Marquesas,  and  more  than  one  thousand  miles  from  the; 
Gambier  Islands,  are  found  hundreds  of  gigantic  stone' 
images,  now  mostly  in  ruins.  They  are  often  forty  feet- 
high,  while  many  seem  to  have  been  larger,  the  crowns  of 
their  heads,  cut  out  of  red  stone,  being  sometimes  ten  feet 
in  diameter,  while  even  the  head  and  neck  of  one  is  said 
to  have  been  twenty  feet  high.  The  island  containing 
these  remarkable  works  has  an  area  of  about  thirty  square 
miles,  and  as  the  smallest  image  is  about  eight  feet  high, 
weighing  four  tons,  and  as  the  largest  must  weigh  over  a 
hundred  tons  or  much  more,  their  existence  implies  a  large 
population,  abundance  of  food,  and  an  established  govern- 
ment which  so  small  an  island  could  not  supply.  (Hyslop.) 

7.  We  observe  very  frequently  that  very  poor  handwrit- 
ing characterizes  the  manuscripts  of  able  men,  while  the 
best  handwriting  is  as   frequent  with  those  who  do  little 
mental  work  when  compared  with  those  whose  penmanship 
is  poor.     We  may,  therefore,  infer  that  poor  penmanship 
is    caused   by   the  influence   of   severe   mental   occupation. 
(Hyslop.) 

8.  In  the  following  instances  crystallization  takes  place: 
the  freezing  of  water;  cooling  and  solidifying  of  molten 
metals   and  minerals;   deposition  of  salts    from   solutions; 
volatilization   of   solutions;   deposition   of   solids   from  the 
gaseous  state,  as  iodine;  pressure;  slow  internal  change,  as 
in  rocks;  the  transformation  of  metals  from  the  tough  to 
the   brittle    condition,    by   hammering;    vibration,    and    re- 
peated heatings  and  coolings.     We  may  then  conclude  that 
the  cause  of  crystallization  is  the  increased  scope  and  oper- 
ation of  the  molecular  or  solid-forming  cohesion.     (Bain.) 

9-  When  the  barometer  was  carried  to  the  top  of  the  Puy 
de  Dome  it  was  found  that  the  mercury  stood  lower  than 
before.  It  was  inferred  that  the  pressure  of  the  air  was 
the  cause  of  the  rise  of  mercury  in  the  tube. 

10.  The  chemical  action  between  two  substances  is  much 
greater  when  they  are  in  a  liquid  than  when  they  are  in  a 
gaseous  state.     We  may  conclude  that  there  is  an  inverse 
relation  between  cohesion  and  chemical  activity. 

11.  Goldscheider  proved  that  muscular   sensations   play 
no  considerable  part  in  pur  consciousness  of  the  movement 


108  INDUCTION* 

of  our  limbs,  by  having  his  arm  suspended  in  a  frame  and 
moved  by  an  attendant.  Under  these  circumstances,  where 
no  work  devolved  on  the  muscles,  he  found  that  he  could 
distinguish  as  small  an  angular  movement  of  the  arm  as 
when  he  moved  and  supported  it  himself. 

He  also  proved  that  the  chief  source  of  movement-con- 
sciousness is  pressure-sensations  from  the  inner  surface  of 
the  joints,  by  having  his  arm  held  so  that  the  joint  sur- 
faces are  pressed  more  closely  together,  and  finding  that 
a  smaller  movement  was  now  perceptible.  (Creighton.) 

12.  "  That  the  Tempest  belongs  to  the  latest  period  of 
Shakespeare's  literary  activity  is  shown,  inter  alia,  by  the 
absence   of  rhyme,   the   large   number   of   '  run   on '    (un- 
stopped) lines,  the  high  proportion  of  weak  and  light  end- 
ings, and  the  comparative  rarity  of  puns  in  the  low  scenes." 
(Mellone.) 

13.  That  the  feeling  of  effort  is  largely,  if  not  entirely, 
of  peripheral  origin,  appears  from  such  experiments  as  the 
following:     Hold  the  finger  as  if  to  pull  the  trigger  of  a 
pistol.     Think  vigorously  of  bending  the  finger,  but  do  not 
bend  it.     An  unmistakable  feeling  of  effort  results.      Re- 
peat the  experiment,  and  notice  that  the  breath  is  involun- 
tarily held,  and  that  there  are  tensions  in  the  other  mus- 
cles.     Repeat  the   experiment  again,  taking  care  to  keep 
the  breathing  regular  and  the  other  muscles  passive.    Little 
or  no  feeling  of  effort  will  now  accompany  the  imaginary 
bending  of  the  finger.     (Ferrier,  quoted  by  Hibben.) 

14.  Sir  Charles  Lyell,  by  studying  the  fact  that  the  rivtr 
Ganges  yearly  conveys  to  the  ocean  as  much  earth  as  would 
form  sixty  of  the  great  pyramids  of  Egypt,  was  enabled 
to  infer  that  the  ordinary  slow  causes  now  in  operation 
upon  the  earth  would  account  for  the  immense  geological 
changes  that  have  occurred,  without  having  recourse  to  the 
less  reasonable  theory  of  sudden  catastrophes.     (Hibben.) 

15.  Count    Rumford   in    1798   proved  that   the   common 
notion  that  heat  was   a  substance  was  false,  by  boring  a 
large   piece   of   brass,   under   great   pressure   of   the   bore, 
whilst  the  brass  was  in  a  gallon  of  water;  and  at  the  end 
of  two  and  one-half  hours  the  water  actually  boiled.     (Hib- 
ben.) 

16.  How  would  you  set  out  to  discover  the  causal  rela- 


EXERCISES  109 

tions  of  the  following  phenomena?     Suggest  instances  and 
indicate  the  method  to  be  used: 

(1)  Heat  and  expansion. 

(2)  Heat  and  friction. 

(3)  Mosquitos  and  malaria. 

(4)  The  tubercle  bacillus  and  consumption. 

(5)  Golden-rod  and  hay  fever. 

(6)  A  rainy  spring  and  mosquitos. 

(7)  The  presence  of  oxygen  and  the  burning  of  a 

candle  flame. 

(8)  Cocaine  and  the  absence  of  pain. 

(9)  Moisture  and  vegetation. 

(10)  The  gulf-stream  and  climate. 

(11)  The  cause  of  the  tides. 

(12)  The  cause  of  the  trade  winds. 

(13)  The  course  of  a  glancing  bullet. 

17.  Cite  ten  cases  of  the  composition  of  causes. 

18.  Cite  ten  of  the  plurality  of  causes. 

19.  Cite  ten  cases  of  counteracting  causes. 

20.  Bring  in  five  cases  illustrating  each  of  the  methods. 


CHAPTER    VII 
VERIFICATION    AND    DEDUCTION 

Verification  and  Deduction. — All  these  methods 
are  means  by  which  a  sound  inference  may  be  drawn  or 
an  inference  already  drawn  may  be  verified.  They  all 
involve  finding  certain  facts  which  inevitably  follow 
from  the  inference  in  question,  and  they  are  not  con- 
clusive if  these  facts  can  be  shown  to  be  consistent  with 
any  rival  hypothesis. 

There  is  another  way  of  testing  the  truth  of  any  in- 
ference ;  if  we  can  show  that  the  inference  follows  from 
something  already  known  we  shall  establish  the  truth 
of  the  inference  itself.  Instead  of  searching  for  the 
consequences  of  the  inferences  and  trying  to  determine 
their  truth,  we  find  a  law  of  which  our  inference  is  it- 
self a  necessary  consequence.  Conversely  if  an  infer- 
ence is  inconsistent  with  a  known  law  it  is  necessarily 
false.  In  applying  this  it  is  necessary  to  remember 
that  many  supposed  laws  have  proved  to  be  false  and 
that  when  an  inference  disagrees  with  a  supposed  law, 
it  may  be  that  the  latter — or  both — must  be  rejected. 
The  fact  that  an  inference  is  consistent  with  known 
laws  does  not  prove  its  truth,  but  only  its  possible 
truth,  for  two  rival  hypotheses  may  be  consistent  with 
all  the  known  facts  and  laws  to  which  they  are  related. 
For  proof,  the  connection  must  be  closer  than  mere  con- 
sistency. The  inference  must  not  only  agree  with  the 
law,  it  must  follow  from  it;  in  other  words,  the  truth 
of  the  law  must  insure  the  truth  of  the  inference, 

HP 


SYSTEMATIC    KNOWLEDGE  111 

An  inference  from  a  law  or  general  principle  to  some 
consequence  of  the  principle  is  a  deductive  inference. 
When  we  reason  in  this  way  we  reason  deductively,  we 
deduce  a  conclusion,  we  employ  deduction. 

Systematic  Knowledge. — -When  we  show  that  an  in- 
ductive inference  is  a  reliable  statement  of  the  relation 
of  certain  phenomena  to  each  other,  or  when  we  show 
that  any  inference  whatever  is  a  consequence  of  some 
general  principle,  we  establish  the  fact  that  the  infer- 
ence with  which  we  are  dealing  belongs  to  a  system  of 
facts  or  truths.1  In  a  system  all  the  parts  and  elements 
are  so  related  that  the  truth  of  one  part  implies  the 
truth  of  the  rest ;  we  cannot  hold  to  one  part  and  reject 
the  rest  without  inconsistency  and  contradiction.  A  sys- 
tem may  consist  of  comparatively  few  members  and  be 
comparatively  simple,  as  in  an  isolated  syllogism,  or  it 
may  be  very  broad  in  its  scope  and  its  internal  relations 
may  be  exceedingly  complex.  For  example,  a  philo- 
sophical system  attempts  to  state  the  laws  which  hold 
for  all  reality. 

We  shall  begin  our  examination  of  systems  with  the 
syllogism.  When  we  argue,  to  use  the  most  ancient  of 
illustrations,  that  "  Socrates  is  mortal  because  all  men 
are  mortal  and  Socrates  is  a  man,"  we  are  basing  the 
truth  of  our  conclusion  upon  a  universal  proposition, 
"  All  men  are  mortal,"  and  the  further  proposition, 
"  Socrates  belongs  to  the  class  men." 

Criticism  of  the  Syllogism. —  It  might  be  urged,  as 
an  objection  to  the  syllogism,  that  "it  gives  us  no  new 

l  Professor  Hibben  in  his  Logic,  Deductive  and  Inductive, 
makes  much  use  of  this  conception  in  discussing  the  nature  of 
deduction  and  induction. 


VERIFICATION    AND    DEDUCTION 

information ;  if  the  conclusion  is  really  contained  in 
the  major  premise,2  as  it  must  be  if  the  reasoning  is  to 
be  valid,  why  go  to  the  trouble  of  making  a  syllogism? 
We  knew  beforehand  that  all  members  of  the  class 
designated  by  the  subject  were  included  in  that  desig- 
nated by  the  predicate,  or  possessed  the  quality,  rela- 
tion, or  whatever  it  may  be,  for  which  the  predicate 
stands;  if  we  did  not  know  that  Socrates  was  mortal, 
how  could  we  say  that  all  men  are  mortal?  Therefore, 
it  is  a  matter  of  course  that  the  subject  of  the  conclu- 
sion, which  is  included  in  the  subject  of  the  major 
premise,  will  have  that  predicate.  This  objection  would 
lead  to  the  condemnation  of  such  a  science  as  geom- 
etry, for  all  its  conclusions  are  contained  in  its  postu- 
lates and  axioms.  Still  we  do  get  information  by 
means  of  such  processes. 

We  may  know  it  to  be  a  general  law  that  all  iron 
compounds  have  certain  properties  without  knowing 
the  chemical  composition  of  a  compound  we  have  in  our 
hands ;  as  soon  as  we  discover  that  it  is  a  compound  of 
iron,  we  can  draw  our  conclusion.  Of  course,  if  our 
major  premise  were  not  a  law,  our  conclusion  would 
not  be  trustworthy.  If  the  general  statement  about 
iron  compounds  were  an  unverified  inductive  inference, 
then  we  could  not  state  it  with  certainty  so  long  as 
we  were  not  sure  that  the  present  compound,  if  it  proves 
to  be  iron,  would  possess  the  given  properties.  If  all 
inductive  inferences  were  simply  enumerative  or  collec- 
tive judgments  (page  86),  if  "perfect  induction" 
were  the  ideal  form  of  induction,  then  there  would  be 
ground  for  the  objection  we  have  mentioned.  But  if 

2  The  universal  proposition  on  which  the  reasoning  is  based,  in 
this  case,  "All  men  are  mortal."  is  called  the  major  premise. 


VALUE    OF    THE    SYLLOGISM          113 

we  may  know  that  whenever  a  given  phenomenon  oc- 
curs, a  certain  circumstance  must  inevitably  be  pres- 
ent, or  that  any  two  properties  are  invariably  con- 
nected, we  have  information  which  will  apply  to  many 
cases  of  whose  character  we  may  yet  be  in  ignorance. 
The  syllogism  is  the  typical  form  of  reasoning.  The 
quotation  which  follows  is  from  Professor  James's  Psy- 
chology; it  states  the  claim  that  reasoning  is  precisely 
that  form  of  mental  activity  which  does  enable  us  to 
deal  with  new  situations,  with  novel  data. 

"  A  thing  inferred  by  reasoning  need  neither  have 
been  an  habitual  associate  of  the  datum  from  which  we 
infer  it,  nor  need  it  be  similar  to  it.  It  may  be  a  thing 
entirely  unknown  to  our  previous  experience,  something 
which  no  simple  association  of  concretes  could  ever  have 
evoked.  The  great  difference,  in  fact,  between  that 
simple  kind  of  rational  thinking  which  consists  in  the 
concrete  objects  of  past  experience  merely  suggesting 
each  other  and  reasoning  distinctly  so-called  is  this: 
that  whilst  empirical  thinking  is  only  reproductive, 
reasoning  is  productive.  An  empirical,  or  *  rule-of- 
thumb,'  thinker  can  deduce  nothing  from  data  with 
whose  behaviour  and  associates  in  the  concrete  he  is  un- 
familiar. But  put  a  reasoner  amongst  a  set  of  con- 
crete objects,  which  he  has  neither  seen  nor  heard  of 
before,  and  with  a  little  time,  if  he  is  a  good  reasoner, 
he  will  make  such  inferences  from  them  as  will  quite 
atone  for  all  his  ignorance.  Reasoning  helps  us  out 
of  unprecedented  situations — situations  for  which  all 
our  common  associative  wisdom,  all  the  *  education  * 
which  we  share  in  common  with  the  beasts,  leaves  us 
without  resource."  Psychology,  Briefer  Course,  page 


114      VERIFICATION    AND    DEDUCTION 

As  soon  as  we  see  that  the  present  case  belongs  to  a 
certain  class  or  is  of  a  certain  type,  the  laws  which  are 
known  to  apply  to  that  class  or  type  may  immediately 
be  applied  to  it. 

How  Propositions  are  Related  to  each  other — 
The  syllogism  as  illustrated  above  shows  that  a  univer- 
sal judgment  may  be  made  the  basis  for  certain  other 
statements.  There  are  several  kinds  of  syllogisms,  but 
before  discussing  these  it  will  be  well  to  examine  propo- 
sitions generally  with  a  view  to  discovering  what  rela- 
tions different  kinds  of  statements  bear  to  each  other 
and  whether  there  may  not  be  other  ways  than  that 
illustrated  in  the  syllogism,  in  which  one  statement  may 
be  made  the  basis  for  another.  We  have  already  dis- 
cussed four  kinds  of  propositions ;  those  which  are 
universal  and  affirmative,  universal  and  negative,  par- 
ticular and  affirmative,  and  particular  and  negative.  It 
will  be  remembered  that  the  symbols  for  these  were  A, 
E,  I,  and  O  respectively.  Their  relations  to  each  other 
are  best  shown  by  means  of  what  is  known  as  the 
"  Square  of  Opposition,"  a  diagram  which  has  remained 
practically  unchanged  since  the  time  of  Aristotle. 
(All  x  is  y)  (No  x  is  y) 

A  Contraries  E 


1 
* 


I  Subcontraries  O 

(Some  x  is  y)  (Some  x  is  not  y) 


RELATIONS    OF    OPPOSITION  115 

Let  us  take  as  an  illustration  of  the  A  proposition,  "  All 
men  are  rational."  Its  contrary  will  be  "  No  men  are 
rational."  What  exactly  are  the  relations  between 
these  two  propositions?  If  A  be  true,  it  is  obvious  that 
E  will  be  false,  and  if  E  be  true  A  will  be  false.  But 
if  A  be  false,  what  about  E?  It  may  be  true  or  false, 
for  the  falsity  of  A  leaves  those  two  possibilities ;  in 
other  words,  the  truth  or  falsity  of  E  is  undetermined. 
Similarly  of  A,  if  E  be  false.  If  either  be  false,  there  is 
a  middle  ground;  thus,  it  may  be  that  some  men  are 
rational  and  some  are  not.  Two  propositions  are  con- 
trary when  only  one  can  be  true  and  both  can  be  false. 

"All  men  are  rational"  (A),  and  "  Some  men  are 
not  rational"  (O),  are  contradictory  propositions.  If 
A  be  true,  O  will  be  false,  and  if  A  be  false,  O  will  be 
true ;  likewise  if  O  be  true,  A  will  be  false,  and  if 
O  be  false  A  will  be  true.  There  is  no  middle  ground ; 
there  is  no  third  possibility.  Only  one  can  be  true,  and 
only  one  can  be  false,  or  in  other  words,  both  cannot 
be  true  and  both  cannot  be  false.  Two  propositions  are 
contradictory  when  they  are  exact  opposites;  one  must 
be  true  and  the  other  must  be  -false. 

Of  sub-contrary  propositions,  both  may  be  true,  but 
only  one  can  be  false.  The  propositions,  "  Some  men 
are  rational  "  and  "  Some  men  are  not  rational,"  are 
in  the  relation  of  sub-contraries.  If  either  be  false  the 
other  must  be  true,  and  if  one  be  true  the  other  may  be 
true  also ;  both  may  be  true,  and  one  must  be.  The 
propositions  I  and  O  are  consistent,  whereas  contraries 
and  contradictories  are  inconsistent. 

4  Two  propositions  which  are  to  stand  in  a  relation  of  op- 
position to  each  other  must  have  identical  terms.  This  is  true 
in  the  traditional  treatment,  but  exceptions  will  be  noted  later. 


116      VERIFICATION    AND    DEDUCTION 

In  the  case  of  subalterns,  both  propositions  are  of 
the  same  quality,  but  they  differ  in  quantity.  "  All 
men  are  rational "  and  "  Some  men  are  rational  "  are 
subalterns.  //  the  universal  be  true  the  particular  will 
of  course  be  true  also;  but  if  the  universal  be  false  the 
other  is  left  indeterminate;  it  may  be  true  or  it  may  be 
false.  On  the  other  hand,  if  the  particular  proposition 
be  false,  the  universal  will  necessarily  be  false  too;  if 
it  is  false  that  "  Some  men  are  rational,"  it  cannot  be 
true  that  "  All  men  are  " ;  but  if  the  particular  be  true 
it  is  by  no  means  certain  that  the  other  will  be.  Thus, 
if  we  know  that  some  men  are  rational,  that  does  not 
give  us  a  right  either  to  affirm  or  to  deny  that  all  men 
are  rational ;  in  other  words,  the  truth  of  the  universal 
is  left  indeterminate. 

To  summarize:  contrary  propositions  are  such  that 
only  one  can  be  true,  and  both  may  be  false. 

Contradictory  propositions  are  so  related  that  one 
must  be  true  and  the  other  must  be  false. 

Sub-contraries  may  both  be  true,  but  only  one  can 
be  false. 

Subalterns  may  both  be  true  or  both  false.  The 
truth  of  the  universal  assures  the  truth  of  the  par- 
ticular, but  the  falsity  of  the  universal  does  not  in- 
volve the  falsity  of  the  particular;  the  falsity  of  the 
particular  involves  the  falsity  of  the  universal,  but  the 
truth  of  the  particular  does  not  assure  the  truth  of  the 
universal. 

Relations  of  Opposition  among  Propositions  which 
have  not  Identical  Terms. —  These  relations  are  most 
easily  detected  between  propositions  which  have  the 
same  subject  and  the  same  predicate,  but  it  is  possible 


RELATIONS    OF    OPPOSITION  117 

to  find  them  in  propositions  which  do  not  answer  to  this 
description.  The  propositions,  "  All  men  are  rational  " 
and  "  All  men  are  idiots,"  are  contraries.  Both  cannot 
be  true,  but  both  may  be  false. 

Or  again,  "  Socrates  was  the  wisest  of  the  Greeks  " 
and  "  Aristotle  was  the  wisest  of  the  Greeks,"  are  con- 
trary propositions.  Only  one  of  them  could  be  true, 
while  both  might  be  false. 

This  will  be  found  to  be  the  case  with  a  great  many 
inconsistent  propositions.  In  fact  all  inconsistent 
propositions  which  are  not  contradictories  are  con- 
traries. Many  pairs  of  such  inconsistent  propositions 
would  not  fit  into  the  square  of  opposition,  for  both 
might  be  affirmative  or  both  might  be  negative.  A  and 
E  propositions  which  have  identical  terms  are  contra- 
ries :  we  need  not  consider  the  meaning  of  the  proposition 
to  discover  that,  for  it  is  evident  from  their  form.  In 
other  cases  we  must  take  into  account  the  meaning  as 
well.  "  A  is  B  "  and  "  A  is  not  B  "  are  contraries  so 
long  as  the  meaning  of  the  terms  A  and  B  remains  the 
same,  no  matter  what  that  meaning  is ;  but  the  relation 
between  "  A  is  X  "  and  "  A  is  Y  "  can  be  determined 
only  after  we  know  the  meaning  of  X  and  Y.  If  we 
learn  that  X  and  Y  are  opposites  we  can,  of  course,  re- 
state our  second  proposition,  "A  is  Y,"  in  the  form 
"  A  is  not  X,"  the  contrary  of  "  A  is  X."  If  X  and 
Y  prove  to  be  the  same  or  similar  in  meaning  the  two 
original  propositions  are  of  course  consistent. 

Subject  and  predicate  may  both  be  different;  e.  g., 
"  Oxygen  is  heavier  than  nitrogen  "  and  "  Nitrogen  is 
heavier  than  oxygen."  Only  one  cannot  be  true ;  both 
might  be  false.  If  two  propositions,  alike  in  quality, 


118      VERIFICATION    AND    DEDUCTION 

have  the  same  subject  but  have  predicates  which  are 
complete  opposites,  as  X  and  not-X,  the  propositions 
will  be  contradictories.  Such  pairs  of  terms  as  "  ra- 
tional and  non-rational,"  "  square  and  not-square,"  are 
examples. 

Cases  sometimes  occur  in  which  propositions  having 
the  same  predicates  but  different  subjects  will  be  con- 
tradictory in  meaning:  thus,  "  Man  alone  is  rational "; 
"  Some  being  besides  man  is  rational." 

Similarly,  propositions  with  unlike  terms  may  stand 
in  the  relation  of  sub-contraries.  For  example :  "  Some 
men  are  rational  "  and  "  Some  men  are  irrational,"  and 
66  Simple  substances  make  up  a  large  part  of  the 
earth's  crust  "  and  "  Compound  substances  make  up 
a  large  part,  etc.,"  are  pairs  of  sub-contraries. 

And  likewise  in  the  case  of  subalterns :  for  example, 
"  All  men  are  vertebrates  "  and  "  All  men  are  mam- 
mals " ;  "  No  mental  states  can  be  weighed,"  "  No  emo- 
tions can  be  weighed."  The  relation  of  subaltern  may 
hold  between  two  propositions  even  if  one  of  them  is  not 
universal.  Thus,  "  Most  books  are  worthless "  and 
"  Some  books  are  worthless."  Of  course,  "  The  recent 
novels  are  worthless,"  is  not  necessarily  a  subalterna.te 
of  either  of  these  propositions. 

Singular  propositions  require  special  notice.  "  Soc- 
rates was  the  noblest  of  men  "  and  "  Socrates  was  not 
the  noblest  of  men  "  are  apparently  contrary  propo- 
sitions, but  as  a  matter  of  fact  they  are  contradictories. 
Singular  propositions  which  have  the  same  terms  are 
never  contraries  except  in  form.  On  the  other  hand, 
"  Socrates  was  an  Athenian  "  and  "  Socrates  was  a 
Spartan  "  are  contraries. 

Conversion. — A  proposition  is  the  verbal  expression 


CONVERSION  119 

of  a  judgment,  and  a  judgment  is  an  act  of  thought 
wherein  we  assert  that  certain  relations  hold  among  cer- 
tain objects  of  thought,  as,  A  is  B,  A  Is  not  B,  some  A 
is  Y,  and  so  on.  Now  it  is  often  possible  to  formulate 
other  propositions  which  are  equivalent  to  these  or 
which  are  obviously  true  if  the  original  proposition  be 
true.  The  proposition,  "  No  conic  sections  are  rectan- 
gular figures,"  is  equivalent  to  "  No  rectangular  figures 
are  conic  sections."  The  only  difference  between  the 
two  is  in  the  order  of  the  terms.  The  original  subject 
and  predicate  have  been  interchanged.  This  process 
is  known  as  Conversion.  The  proposition  just  con- 
verted was  an  E  proposition  and  all  E  propositions  can 
be  converted. 

Again,  the  proposition,  "  Some  metals  are  elements  " 
can  be  converted  into  "  Some  elements  are  metals." 
Both  are  I  propositions.  From  the  proposition,  "  Some 
quadrupeds  are  horses,"  we  can  get  only  "  Some  horses 
are  quadrupeds,"  We  happen  to  know  that  the  same 
could  be  said  of  all  horses,  but  we  do  not  get  that 
knowledge  from  the  original  proposition.  The  original 
statement  is  affirmative  and  affirmative  propositions,  as 
we  have  seen,  do  not  give  information  about  the  whole 
of  the  predicate.  But  the  statement,  "All  horses  are 
quadrupeds,"  being  universal,  affirms  something  about 
the  whole  class  horses. 

The  first  general  rule  of  conversion  is  that  no  term 
may  be  distributed  in  the  converse  "which  was  not  dis- 
tributed in  the  original  proposition.  A  proposition, 
then,  such  as  "  All  A  propositions  are  universal,"  can 
have  as  its  converse  only  an  I  proposition,  "  Some  uni- 
versal propositions  are  A  propositions." 

Each  of  the  propositions  dealt  with  above  has  had  as 


120      VERIFICATION    AND    DEDUCTION 

its  converse  another  proposition  having  the  same 
quality.  In  all  cases  the  converse  of  a  proposition  must 
have  the  same  quality  as  the  original  proposition.  This 
is  a  second  rule  of  conversion.  From  this  and  the  for- 
mer rule  it  follows  that  the  0  proposition  can  have  no 
converse.  Its  subject  is  undistributed  and  its  quality 
negative ;  but  in  the  converse,  the  original  subject,  hav- 
ing become  the  predicate  of  a  negative  proposition, 
would  be  distributed,  a  violation  of  the  first  rule. 

Proposition  Converse 

The  converse  of  A  is  I:        All  S  is  P;  Some  P  is  S. 

The  converse  of  I  is  I:    Some  S  is  P;  Some  P  is  S. 

The  converse  of  E  is  E:        No  S  is  P;  No  P  is  S. 
O  has  no  converse. 

The  use  of  Euler's  circles  5  will  help  to  make  these  re- 

A    (Pi's)        All  S  is  P  or  (at  least)  some  P  is  S. 

E    (S)  ©     No  S  is  P  or  no  P  is  S. 

I  (  <§~p)        (At  least)  some  S  is  P  or  some  P  is  S. 

0    (§?£))      Some  S  is  not  P  but  all  P  may  be  S, 
or  no  P  may  be   S,  or  some  may  be  and  some  may 
not  be. 

lations  clear.  We  see  that  propositions  E  and  I  are 
converted  into  E  and  I ;  in  technical  language  they  are 
converted  "  simply."  A  can  be  converted  only  into  I ; 

5  The   forms  here  used  are  taken  from  Hyslop's   Elements  of 
Logic. 


OBVERSION 

that  is,  it  is  converted  into  a  proposition  which  is  less 
general  than  itself,  into  a  particular  proposition.  Such 
conversion  is  known  as  conversion  by  limitation  or  per 
accidens. 

Obversion. —  Again,  we  may  find  for  all  ordinary 
propositions  an  equivalent  of  the  opposite  quality :  "  All 
men  are  wise  "  is  equivalent  to  "  No  men  are  unwise  "  \ 
"  Some  men  are  just  "  can  be  expressed  as  "  Some  men 
are  not  unjust  " ;  "  No  animals  are  moral  "  as  "  All  ani- 
mals are  unmoral " ;  "  Some  men  are  not  honest  "  as 
"  Some  men  are  dishonest."  It  will  be  noticed  that  in 
every  case  the  subject  is  unchanged.  (In  "  All  men  are 
wise,"  and  "  No  men  are  wise,'"'  .the  subject  is  in  both 
cases  "  All  men  " ;  the  "  No  "  belongs  to  the  statement 
as  a  whole,  not  to  the  subject.  The  negative  of  "  All 
men  "  would  be  "All  who  are  not  men.")  This  process 
is  called  Obversion.  The  quality  of  the  proposition  if 
changed  and  the  predicate  of  the  obverse  is  the  com- 
plete opposite  of  the  predicate  of  the  original  proposi- 
tion. 

Proposition  Obverse 

The  obverse  of  A  is  EJ   All  S  is  P;  No  S  is  not-P. 

The  obverse  of  I  is  O:     Some  S  is  P;  Some  S  is  not  not-P. 

The  obverse  of  E  is  A:    No  S  is  P;  All  S  is  not-P. 

The  obverse  of  O  is  I:     Some  S  is  not  P;  Some  S  is  not-P. 

If  the  predicate  in  the  original  proposition  be  nega- 
tive, as  non-conductor,  it  will  be  replaced  in  the  obverse 
by  the  corresponding  positive  term,  conductor.  "  Some 
S  is  not-P  "  will  have  as  its  obverse  "  Some  S  is  not 
P."  Difficulty  is  likely  to  arise  with  regard  to  the 
predicate  and  its  opposite.  For  example,  the  proposi- 
tion, "  No  animals  are  moral,"  is  not  equivalent  to  "  All 


VERIFICATION    AND    DEDUCTION 

animals  are  immoral."  They  may  be  neither  moral  nor 
immoral.  The  predicate  in  the  new  proposition  must 
be  completely  opposite  or  contradictory  to  the  original 
predicate.  Sometimes  it  can  not  be  expressed  simply. 
For  example,  take  the  proposition,  "  The  president  is 
the  nation's  highest  executive  officer."  In  the  obverse 
the  whole  of  the  predicate  must  be  made  negative,  not 
simply  "  highest  "  or  "  executive  "  or  "  officer."  It 
might  read,  "  The  president  is  not  any  one  who  is  not 
the  nation's  highest  executive  officer." 

The  following  symbols  may  be  employed  to  indicate 
the  relations  considered  in  obversion.  Suppose  we  have 
a  proposition  with  the  predicate  P  or  not-P.  Every- 
thing in  the  universe  either  has  or  has  not  the  predicate 
P,  that  is,  everything  has  one  or  the  other  of  the 
predicates  P  and  not-P.  We  may  represent  this  fact  by 
a  circle  divided  into  two  compartments,  thus : 


Then  any  given  thing  will  fall  into  one  or  the  other  of 
those  compartments.  If  our  proposition  asserts  that 
it  falls  into  one,  that  is  tantamount  to  asserting  that  it 
falls  outside  the  other ;  the  latter  assertion  would  be 
the  obverse  of  the  former.  S  is  P,  implies  that  S  is  not 
not-P ;  T  is  not-P,  implies  that  T  is  not  P. 

Contraposition. — These  changes  in  the  form  of  prop- 
ositions may  both  be  present  together  and  repeatedly. 
Let  us  take  the  proposition,  "  No  men  are  immortal." 


CONTRAPOSITION 

The  obverse  would  be,  "  All  men  are  mortal  " ;  the  con- 
verse of  this,  "  Some  mortals  are  men  " ;  the  obverse  of 
this  again,  "  Some  mortals  are  not  not-men "  (not 
anything  else  than  men)  ;  and  this,  being  an  O  propo- 
sition, has  no  converse.  We  might,  of  course,  have 
begun  with  conversion. 

What  is  known  as  Contraposition  is  equivalent 
to  obversion  plus  conversion.6  The  contrapositive  of 
"  No  men  are  immortal "  is  "  Some  mortals  are  men  " ; 
the  contrapositive  of  "  All  men  are  mortal  "  would  be 
"  No  immortals  are  men."  In  the  contrapositive  the 
subject  is  the  opposite  of  the  original  predicate,  the 
predicate  is  the  original  subject,  and  the  quality  of  the 
proposition  is  the  opposite  of  that  of  the  original  prop- 
osition. An  application  of  the  rules  for  conversion  will 
show  that  the  I  proposition  has  no  contrapositive.  The 
contrapositives  of  the  various  propositions  are  as  fol- 
lows: 

Proposition  Contrapositive 

A,  contrapositive  E:  All  S  is  P;  No  not-P  is  S. 
I,  no  contrapositive. 

E,  contrapositve  I:  No  S  is  P;  Some  not-P  is  S. 

O,  contrapositive  I:  Some  S  is  not  P;  Some  not-P  is  S. 

In  Conversion,  Obversion,  and  Contraposition  we 
have  found  certain  variations  in  the  forms  in  which  a 
given  thought  content  can  be  expressed.  Such  varia- 
tions in  the  form  of  expression  help  to  make  clearer 
just  what  the  content  of  the  judgment  really  is.  In 
these  processes  the  changes  in  the  form  of  expression 
are  due  to  a  change  in  the  order  of  subject  and  predi- 

6  Some  logicians  add  a  second  obversion.    See  Hibben,  Logic. 


VERIFICATION   AND    DEDUCTION 

cate  or  a  change  in  the  quality  of  predicate  and  copulas 
or  both. 

EXERCISES 

1.  Give  contrary,  contradictory,  and  subaltern  of  each  of 
the  propositions  in  Exercises  "  5,"  pages  62-65 ;  where  it  is 
not  possible  to  give  all,  state  the  reason  why. 

2.  Classify  the  subjoined  propositions  into  the  four  fol- 
lowing groups: 

1.  Those  which  can  be  inferred  from   (1). 

2.  Those  from  which  (1)  can  be  inferred. 

3.  Those  which  do  not  contradict  (1)   but  cannot  be 

inferred  from  it. 

4.  Those  which  contradict  (1). 

(1)  All  just  acts  are  expedient  acts.- 

(2)  No  expedient  acts  are  unjust. 

(3)  No  just  acts  are  inexpedient. 
(4-)  All  inexpedient  acts  are  unjust. 

(5)  Some  unjust  acts  are  inexpedient. 

(6)  No  expedient  acts  are  just. 

(7)  Some  inexpedient  acts  are  unjust. 

(8)  All  expedient  acts  are  just. 

(9)  No  inexpedient  acts   are  unjust. 

(10)  All  unjust  acts  are  inexpedient. 

(11)  Some  inexpedient  acts  are  just  acts. 

(12)  Some  expedient  acts  are  just. 

(13)  Some  just  acts  are  expedient. 

(14)  Some  unjust  acts  are  expedient.    (Jevons.) 

3.  Give  the  converse,  the  obverse,  and  the  contrapositive 
of  each  of  the  following  propositions : 

(1)  All  who  were  present  were  unprepared. 

(2)  No  wise  man  would  undertake  such  a  task. 

(3)  Not  to  make  the  attempt  is  to  confess  yourself 

a  coward. 

(4)  Charity  begins  at  home. 

(5)  No  statesman  could  have  stooped  to  such  a  deed. 

(6)  Only  a  fanatic  believes  in  panaceas. 

(7)  Discontent   is    frequently   a   symptom   o£   ineffi- 

ciency. 


EXERCISES  125 

(8)  A  revolution  is  a  surgical  operation  which  self- 

appointed  healers  of  social  diseases  are  very 
ready  to  recommend  as  a  preliminary  to  every 
cure. 

(9)  Uneasy  rests  the  head  which  wears  a  crown. 

(10)  All  organic  substances  contain  carbon. 

(11)  Better  late  than  never. 

(12)  Not  many  of  the  metals  are  lighter  than  water. 
4.  State  the  relation  of  each  of  the  following  proposi- 
tions to  the  succeeding  one: 

(1)  All  the  metals  are  elements. 

(2)  No  metals  are  non-elements. 

(3)  No  non-elements  are  metals. 

(4)  All  non-elements  are  not-metals. 

(5)  All  metals  are  elements. 

(6)  Some  elements   are  metals. 

(7)  Some  metals  are  elements. 

(8)  No  metals  are  elements.     (Hyslop.) 


CHAPTER    VIII* 
THE    SYLLOGISM 

The  Principles  of  Syllogistic  Reasoning. — Let  us  re- 
turn to  the  examination  of  the  syllogism.  Every  com- 
plete syllogism  contains  three  propositions  and  only 
three.  They  are  a  major  premise,  a  minor  premise  and 
a  conclusion.  In  the  syllogism,  "  All  men  are  mortal ; 
Socrates  is  a  man;  therefore  Socrates  is  mortal,"  the 
first  proposition  is  the  major  premise,  the  second  is  the 
minor  premise,  and  the  third  is,  of  course,  the  conclu- 
sion. The  major  premise  is  the  broad  foundation  on 
which  the  reasoning  rests.  It  is  a  universal  proposi- 
tion in  syllogisms  of  this  form.  It  may  be  either  affirm- 
ative or  negative.  Thus  we  may  have,  "  No  men  are 
immortal ;  Socrates  is  a  man ;  therefore  Socrates  is  not 
immortal."  The  major  premise  asserts  that  the  whole 
of  a  certain  class  is  included  in  another  class  or  excluded 
from  it,  or  it  assigns  a  certain  predicate  to  the  whole 
of  a  certain  subject.1  The  minor  premise  asserts  that 
certain  things  are  included  in  the  first  class;  and  the 
conclusion  applies  to  these  things  the  assertion  which 
was  made  about  the  first  class. 

*This  chapter  may  be  omitted.  The  traditional  treatment  is 
given  in  chap.  ix. 

iWe  have  seen  that  all  propositions  may  be  regarded  as  stat- 
ing a  relation  between  classes,  and  that  this  way  of  regarding 
them  is  most  useful  and  convenient.  But  other  types  of  rela- 
tions between  subject  and  predicate  exist  and  should  not  be 
forgotten. 

126 


THE    FIRST    FIGURE 

Behind  this  reasoning  lies  the  principle  called  the 
Dictum  de  Omni  et  Nullo;  i.  e.,  "  Whatever  state- 
ment may  be  made  with  regard  to  a  class  taken  gen- 
erally may  be  made  of  each  and  every  member  of  that 
class"  or  "  Whatever  is  true  of  each  of  the  members 
of  a  class  will  be  true  of  everything  found  to  be  a 
member  of  that  class." 

The  application  of  this  principle  in  the  two  syllo- 
gisms employed  for  illustration  is  perhaps  obvious,  but 
it  may  be  well  to  represent  the  relation  of  the  various 
terms  graphically.  For  this  purpose  Euler's  diagrams 
are  valuable. 


The  class  men  is  first  included  in  the  class  mortal; 
the  individual  Socrates  is  then  included  in  the  class 
men  and  must  in  consequence  be  included  in  the  class 
mortal.  In  the  second  case  men  is  excluded  from  im- 
mortal and  hence  Socrates,  who  is  included  in  men,  will 
necessarily  be  excluded  from  immortal. 

It  will  readily  be  seen  that  (1)  the  minor  premise  in 
a  syllogism  of  this  sort  cannot  be  negative.  A  nega- 
tive minor  premise  would  assert  that  something  did  not 
belong  to  the  class  indicated  by  the  subject  of  the  major 
premise,  and  would  give  no  ground  for  a  further  con- 
clusion. The  fact  that  something  is  true  of  a  whole 
class  of  objects  does  not  tell  us  whether  it  will  or  will 


128  THE    SYLLOGISM 

not  be  true  of  some  things  not  included  in  that  class. 
Thus  the  premises,  "  All  men  are  rational  beings ; 
monkeys  are  not  men,"  do  not  warrant  the  conclusion 
that  monkeys  are  not  rational.2  Other  conclusions  are 


possible  and  we  could  not  prove  this  one  without  using 
information  not  contained  in  our  premises.  If  we  tried 
to  prove  it  by  those  premises  alone,  our  reasoning 
would  be  invalid.  An  invalid  syllogism  is  one  in  which 
the  conclusion  is  not  proved  or  made  necessary  by  the 
premises.  The  conclusion  may  be  true,  but  the  func- 
tion of  the  syllogism  is  to  furnish  a  conclusion  which 
must  be  true  if  the  premises  are  true.  Reasoning  which 
does  not  prove  the  conclusion  is  fallacious,  or  in  other 
words,  it  contains  a  fallacy. 

We  have  seen  that  the  minor  premise  in  a  syllogism  of 
this  form  cannot  be  negative.  It  will  be  obvious  that 
(£)  if  the  major  premise  be  affirmative  the  conclusion 
must  be  affirmative  and  that  if  the  premise  be  negative 
the  conclusion  must  be  negative.  If  we  affirm  something 
of  a  whole  class  we  cannot  deny  it  of  a  part  of  the 

2  These   diagrams    may   be    employed   in   illustrating   the   later 
rules  also. 


THE    SECOND    FIGURE 

class,  and  if  we  deny  it  of  the  whole  class  we  cannot 
assert  it  of  a  part.  It  is  true  also  that  (3)  the  major 
premise  cannot  be  particular.  If  we  have  the  premises, 
"  Some  animals  can  be  domesticated ;  the  wolf  is  an 
animal,"  we  are  obviously  not  justified  in  concluding 
that  the  wolf  can  be  domesticated. 

And  again  (4)  if  the  minor  premise  be  particular,  the 
conclusion  cannot  be  universal;  it  must  be  particular 
too.  From  the  premises,  "  All  works  of  art  are  valu- 
able; some  of  the  objects  in  this  collection  are  works 
of  art,"  we  cannot  conclude  that  all  the  objects  in  this 
collection  are  valuable.  In  no  case  can  our  conclusion 
contain  more  than  was  contained  in  the  premises. 

Syllogistic  Proof. — In  examining  syllogistic  reason- 
ing the  first  question  is  not  "  Is  the  conclusion  true?  " 
but  "  Does  the  conclusion  follow  necessarily  from  the 
premises?  "  If  the  syllogism  of  this  form  correctly 
applies  the  Dictum  de  Omni  et  Nullo  the  reasoning  is 
valid.  A  syllogism  of  this  form  is  said  to  be  in  the 
First  Figure,  and  this  is  the  only  form  of  syllogism 
which  can  be  used  to  prove  a  universal  affirmative  prop- 
osition. 

A  Second  Type  of  Syllogism. — There  are  sev- 
eral other  varieties  of  syllogisms,  each  having  certain 
special  principles  of  its  own.  The  one  next  to  be  dis- 
cussed is  used  to  prove  that  two  facts  or  groups  of 
facts  are  not  the  same ;  it  proves  negative  conclusions 
and  only  those.  Its  Principle  is  this:  if  one  of  two 
things  is  included  in  a  class  from  which  the  other  is 
excluded,3  these  things  are  excluded  from  each  other. 
To  illustrate :  "  Every  college-bred  man  has  read  that 

s  Or  if  one  has  a  predicate  which  the  other  lacks. 


130  THE    SYLLOGISM 

book;  this  man  has  not  read  the  book;  therefore,  this 
man  is  not  college-bred."  The  fact  that  two  subjects 
are  included  in  the  same  class  or  that  they  possess  the 
same  predicate  does  not,  on  the  other  hand,  prove  that 
they  are  the  same  or  that  they  are  related  in  any  other 
way.  They  might  be  even  identical,  it  is  true,  but  in 
the  conclusion  of  a  syllogism  we  are  entitled  to  include 
only  what  must  be. 

Special  rules. — In  this  sort  of  syllogism  (1)  no  con- 
clusion can  be  drawn  -from  two  affirmative  premises. 
Either  of  the  premises  may  be  negative  and  one  of 
them  must  be.  In  the  illustration  given  above,  the 
minor  premise  was  negative.  We  might  have  "  No  col- 
lege man  would  do  this  deed;  this  man  has  done  it; 
therefore,  he  is  not  a  college  man." 

On  the  other  hand  (2),  both  premises  can  not  be 
negative;  only  one  may  be  negative.  If  two  things 
both  lack  the  same  predicate  that  fact  alone  does  not 
warrant  any  further  statement.  "  No  Indians  are  Cau- 
casians "  and  "  No  Chinamen  are  Caucasians  "  does  not 
furnish  any  basis  for  a  statement  concerning  the  rela- 
tion between  Indians  and  Chinamen. 

(3)  The  major  premise  in  a  syllogism  of  this  sort 
must  be  universal.     If  our  major  premise  were  "  Some 
college  men  are  informed  upon  this  subject,"  it  would 
be  possible  that  some  were  not,  and  the  fact  that  a 
given  man  was  ignorant  of  it  would  not  prove  that  he 
was  not  a  college  man. 

(4)  The  minor  premise  may  be  either  universal  or 
particular;  if  it  is  particular,  the  conclusion  must  be 
particular;  if  it  is  universal,  the  conclusion  may  be  uni- 
versal.   It  is  obvious  that  if  we  make  a  statement  about 
only  a  part  of  the  class  for  which  the  subject  of  the 


MAJOR    AND    MINOR    PREMISES        131 

minor  premise  stands,  we  cannot  make  a  statement 
about  the  whole  of  it  in  the  conclusion.  In  every  syllo- 
gism, the  information  contained  in  the  conclusion  must 
be  furnished  in  the  premises. 

Major  and  Minor  Premises. — It  is  not  always  easy 
to  know  immediately  which  is  the  major  premise  in  a 
syllogism  of  this  form.  There  is,  however,  a  rule  which 
can  be  applied  to  all  syllogisms.  The  major  premise 
is  the  one  which  contains  the  major  term.  The  major 
term  is  the  predicate  of  the  conclusion.  In  an  affirm- 
ative conclusion  the  subject  may  be  regarded  as  con- 
tained in  the  predicate.  In  the  proposition,  "  All 
triangles  are  geometrical  figures,"  the  class  triangle 
is  included  in  the  class  geometrical  figures.  The  latter 
term  is  the  major  because  it  stands  for  the  wider  class. 
In  negative  propositions,  the  predicate  is  not  neces- 
sarily wider ;  in  the  proposition,  "  No  conic  sections  are 
triangles,"  the  predicate  is  not  wider  than  the  subject. 
Still,  for  the  sake  of  uniformity,  the  predicate  of  the 
conclusion  is  always  called  the  major  term.  The  syllo- 
gism first  discussed  is  a  syllogism  in  the  First  Figure 
and  the  other  is  in  the  Second  Figure. 

The  Third  Figure. — In  the  next  type  of  syllogism, 
the  subject  is  the  same  in  both  premises,  but  the  predi- 
cates are  different,  or  in  other  words,  the  subject  is 
related  by  inclusion  or  exclusion  to  one  -class  in  the 
major  premise  and  to  another  in  the  minor  premise. 
The  Principles  of  the  Figure  might  be  stated  as  follows : 
1.  //  a  class  (or  individual)  is  included  in 
each  of  two  other*classes  those  classes  include 

I      -T  T- 

each  other,  at  least  in  part.     All  X  is  Y  and  I 
all  X  is  Z ;  therefore,  some  Z  is  Y. 

2.  //   a   class    (or   individual)    is   excluded  from   a 


132  THE    SYLLOGISM 

second  class  and  included  in  a  third,  then  a 
flr^  at  least>  °f  the  third  is  excluded  from  the 

second.     No  X  is  Y  and  all  X  is  Z ;  therefore, 
some  Z  is  not  Y.4 

In  some  cases  a  conclusion  is  possible  if  only  a  part 
of  the  subject  is  described  in  one  of  the  premises. 
Some  of  the  special  rules  which  follow  state  the  condi- 
tions in  which  this  is  true.  (1)  One  of  the  premises 
must  be  universal.  For  example,  "  No  precious  metals 
are  soluble  in  sulphuric  acid;  some  precious  metals  are 
soluble  in  nitric  acid;  therefore,  some  things  soluble  in 
nitric  acid  are  not  soluble  in  sulphuric  acid."  If  the 
first  makes  an  assertion  about  only  a  part  of  the  class 
and  the  second  likewise,  we  can  not  be  certain  that  the 
two  parts  are  the  same  and  thus  we  learn  nothing  about 
the  relation  of  their  predicates.  Thus,  "  Some  triangles 
are  scalene  "  and  "  Some  triangles  are  right-angled  " 
are  premises  which  warrant  no  conclusion  regarding  the 
relation  of  scalene  to  right-angled  figures.  (2)  The 
major  premise  in  this  Figure  may  be  either  affirmative 
or  negative.  The  conclusion  will  have  the  same  quality 
as  the  major  premise.  If  "  No  A  is  B,"  and  "  Some  (or 
all)  A  is  C,"  then  "  Some  C  is  not  B  " ;  or  if  "  All  A  is 
B,"  and  "  Some  A  is  C,"  then  "  Some  C  is  B."  (3)  The 
minor  premise  can  not  be  negative.  If  "  All  deer  are 
herbivorous,"  and  '"'  No  deer  are  hollow-horned  ani- 
mals," we  cannot  conclude  that  "  No  hollow-horned 
animals  are  herbivorous."  (4)  The  conclusion  of  a  syl- 
logism in  the  Third  Figure  is,  in  all  cases,  particular. 
From  "  All  men  are  mammals  "  and*"  All  men  are  bi- 


4  The  student  should  test  each  of  the  special  rules  by  the  use 
of  such  diagrams. 


THE    FOURTH    FIGURE  133 

peds  "  we  can  not  conclude  that  "  All  bipeds  are  mam- 
mals." The  fact  that  some  or  all  of  a  certain  class  are 
included  in  another  class  or  possess  a  given  predicate 
(the  minor  premise  asserts  this)  does  give  us  infor- 
mation about  a  part  of  that  predicate,  but  not  about 
the  whole  (it  does  not  distribute  the  predicate)  ;  as 
that  predicate  becomes  the  subject  of  the  conclusion, 
the  conclusion  must  be  a  particular  proposition. 

The  Fourth  Figure. — "The  three  figures  already  dis- 
cussed were  described  by  Aristotle.  The  fourth  is  the 
invention  of  later  logicians  and  is  usually  regarded  as 
much  less  important  than  any  of  the  others.  In  it  the 
minor  premise  states  something  about  the  predicate  of 
the  major  premise,  and  the  conclusion  in  turn  states 
something  about  the  conclusion  of  the  minor  premise. 
Thus,  "  All  great  poems  are  the  products  of  genius ; 
all  the  products  of  genius  are  inimitable ;  therefore,  some 
inimitable  things  are  great  poems."  (If  the  conclu- 
sion were,  "  Great  poems  are  inimitable,"  we  should  have 
a  syllogism  of  the  First  Figure,  and  "  All  the  products 
of  genius,  etc.,"  would  be  the  major  premise).  The 
Principles  of  this  Figure  are:  1.  //  a  class  is  included 
in  a  second  class  and  this  in  turn  is  included  in  a  third, 
then  the  third  will  be  partly  coextensive  with  the  first. 

All  X  is  Y 
All  Y    is  Z 


Some  Z  is  X 

£.  If  a  class  is  excluded  from  a  second  and  the  lat- 
ter is  included  in  a  third,  then  a  part,  at  least,  of  the 
third  will  be  excluded  from  the  -first. 


134  THE    SYLLOGISM 


No  Y  is  X 
All  X  is  Z 


Some  Z  is  not  Y 

3.  If  a  class  is  included  in  a  second  and  the  latter  is 
excluded  from  a  third,  then  the  third  will  be  excluded 
from  the  first. 

All  X  is  Y 
No  Y  is  Z 


No  Z  is  X 

In  the  illustration  we  have  used  it  is  obvious  that  we 
can  not  conclude  that  "  All  inimitable  things  are  great 
poems."  Our  minor  premise  has  not  given  us  any  in- 
formation about  the  whole  of  the  class,  "  inimitable 
things,"  so  we  can  not  have  a  universal  conclusion  in 
this  instance.  If  our  syllogism  were,  "  All  great  poems 
are  the  products  of  genius;  some  products  of  genius 
are  inimitable,"  it  would  be  impossible  to  draw  a  con- 
clusion. Poems  might  not  happen  to  belong  to  the 
things  included  in  the  minor  premise.  The  result  would 
be  similar  if  the  minor  premise  were  "  Some  products 
of  genius  are  not  inimitable."  If  the  minor  premise 
were,  "  No  products  of  genius  are  inimitable,"  we  could 
of  course  conclude  that  no  inimitable  things  were  poems. 
We  can  formulate  this  rule:  (1)  //  the  major  premise 
be  affirmative  the  minor  premise  must  be  universal.  In 
all  these  instances,  the  major  premise  was  the  same  and 
it  was  universal.  Suppose  we  had  "  Some  great  poems 


THE    FOURTH    FIGURE  135 

were  the  products  of  genius."  It  will  be  seen  that  the 
minor  premise,  "  All  works  of  genius,  etc.,"  will  give  a 
valid  conclusion,  but  that  none  of  the  others  will. 
(£)  //  the  major  premise  be  affirmative  and  particular, 
the  minor  premise  must  be  universal  and  affirmative. 
With  the  minor  premise  "  No  products  of  genius  are 
inimitable,"  no  conclusion  can  be  drawn;  since  only 
some  great  poems  have  been  included  in  works  of 
genius,  it  may  well  be  that  some  inimitable  things  may 
be  found  among  those  not  so  included.  (3)  The  major 
premise  may  be  negative.  "  No  great  statesmen  are 
selfish  politicians  ;  some  (or  all)  selfish  politicians  amass 
great  fortunes ;  therefore,  some  persons  who  amass 
great  fortunes  are  not  great  statesmen."  Some  such 
persons  might  be  great  statesmen,  so  far  as  our  pre- 
mises are  concerned;  hence  we  have  no  right  to  con- 
clude that  no  persons  who  amassed  great  fortunes  were 
great  statesmen. 

EXERCISES 

State  the  Figure  and  point  out  the  errors  in  reasoning  in 
the  following  syllogisms: 

(1)  All   wisdom   is    desirable,   but   a   knowledge   of 

slang   is   not  wisdom,   and  is,   therefore,  not 
desirable. 

(2)  Logic    and    mathematics    furnish    good    mental 

training,  and  consequently  the  latter  may  be 
regarded  as  a  branch  of  the  former. 

(3)  Some  athletes  are  susceptible  to  pneumonia,  and 

as   all  these  men   are   athletes   some  of  them 
must  be  susceptible  to  pneumonia. 

(4)  Some  industrious  people  are  also  bright,  for  there 

are  both  bright  and  industrious   students  in 
that  group. 


136  THE    SYLLOGISM 

(5)  Some  statues  are  very  lifelike,  and  no  lifelike 

things  are  contrary  to  the  laws  of  nature; 
hence,  nothing  contrary  to  -';he  laws  of  nature 
is  a  statue. 

(6)  Some  gymnastic  exercises  are  good  for  increasing 

strength,  but  swimming  is  not,  and  hence  is 
not  a  gymnastic  exercise. 

(7)  All    Democrats    voted   against   the   bill,   and   as 

most  of  our  Congressmen  are  Democrats,  they 
must  all  have  voted  against  the  bill. 

(8)  All  M  is  P; 
No  M  is  S; 

/.No  S  is  P. 

(9)  Europeans  cannot  endure  that  climate;  neither 

can  Americans;  hence,  Americans  may  be  re- 
garded as  a  species  of  European. 

(10)  All   ballads   are  interesting,  and   some  interest- 

ing things  are  very  old;  hence,  some  very  old 
things  are  ballads. 

(11)  All  text-books  are  to  be  had  at  this  store,  but 

some  novels   are   not   to  be   had   here,   which 
proves  that  novels   are  not  text-books. 
For  further  examples  see  page  150  and  page  177f. 


CHAPTER    IX 

TRADITIONAL  TREATMENT  OF  THE  SYLLO- 
GISM 

THE  traditional  treatment  of  the  syllogism  is  sim- 
ple though  very  formal.  The  syllogism  is  regarded  as 
a  form  of  reasoning  in  which  each  of  two  terms  is 
compared  with  a  third  and  as  a  result  the  two  terms 
are  found  to  be  related  to  each  other.  Each  of  the 
two  is  compared  with  the  third  in  a  premise.  The  re- 
sult of  the  comparison  is  stated  in  the  conclusion. 

®  is  P) 

>   Premises. 

(§)  is  M) 
•'•  (§)  is   P      Conclusion. 

P  and  S  are  found  to  stand  in  certain  relations  to  M. 
In  this  case  and  in  many  others  we  are  justified  in  as- 
serting a  relation  between  S  and  P :  S  and  P  are  found 
to  be  related  through  M  as  a  medium.  For  this  rea- 
son M  is  called  the  Middle  Term  and  the  syllogism  is 
said  to  embody  Mediate  Reasoning. 

The  validity  of  the  reasoning  is  tested  by  the  appli- 
cation of  a  number  of  rules.  These  rules  have  to  do 
with  the  relation  and  distribution  of  the  several  terms 
in  the  syllogism.  They  are  as  follows: 

1.  Every  syllogism  contains  three  propositions  and 
only  three. 

2.  Every  syllogism  has  three  terms  and  only  three. 
(If  any  term  is  ambiguous  this  rule  is  violated.) 

137 


138     TREATMENT    OF    THE    SYLLOGISM 

3.  The   middle   term   must    be    distributed    at   least 
once. 

4.  No  term  may  be  distributed  in  the  conclusion  which 
was  not  distributed  in  one  of  the  premises. 

5.  From  two  negative  premises  nothing  can  be  in- 
ferred. 

6.  If  one  premise  be  negative,  the  conclusion  must 
be  negative ;  if  both  premises  be  affirmative,  the  con- 
clusion must  be  affirmative. 

7.  From  two  particular  premises  no  conclusion  can 
be  drawn. 

8.  If  one  premise  be  particular,  the  conclusion  must 
be  particular. 

Let  us  examine  these  rules  in  the  order  given. 

1.  With  more  than  three  propositions,  we  should  have 
more  than  a  syllogism,  though  our  reasoning  might  be 
valid. 

2.  The  violation  of  rule  two  gives  rise  to  the  Fallacy 
of  Four  Terms.    Unless  two  of  the  terms  are  confused 
this  fallacy  is  not  likely  to  arise.     No  one  would  try 
to  draw  a  conclusion  from  the  propositions,  "  Socrates 
was  a  philosopher,"  and  "  The  earth  revolves  about  the 
sun."    But  one  might  be  tempted  to  draw  a  conclusion 
from  the  premises,  "  Steel  is  made  from  iron ;  iron  is 
dug  from  the  ground."   Still,  it  would  be  wrong  to  con- 
clude that  steel  is  dug  from  the  ground.     The  terms 
here    are,    "  steel,"    "  (something)    made    from    iron," 
"iron,"  and  "  (something)   dug  from  the  ground." 

3.  The  violation  of  rule  three  gives  rise  to  the  Fal- 
lacy  of    Undistributed  Middle.      Thus,   the   premises, 
"  Some  men  are  brave ;  and  some  men  are  strong,"  do 
not  prove  anything ;  nor  do  these :     "  All  brave  men 


THE    UNDISTRIBUTED    MIDDLE        139 

should  be  respected;  and,  all  just  men  should  be  re- 
spected." 

Let  us  represent  the  middle  term  by  M,  the  minor 
term  (subject  of  the  conclusion)  by  S,  and  the  major 
term  (predicate  of  conclusion)  by  P.  We  are  not  jus- 
tified by  the  premises  in  making  any  statement  about 
the  relation  of  S  and  P,  for  they  may  be  wholly  or 
partially  identical  or  they  may  be  mutually  exclusive. 
But  if  the  middle  term  were  distributed  we  might  be 
able  to  draw  a  conclusion.  If  all  M  is  P  and  all  S  is  M, 
we  may  conclude  that  all  S  is  P. 


Or  if  no  M  is  P  and  all  S  is  M,  then  no  S  is  P. 


An  invalid  syllogism  is  one  in  which  it  is  not  possible 
to  determine  fully  the  relation  of  the  circles  to  each 
other,  since  there  are  conflicting  possibilities.  In  the 
case  of  Undistributed  Middle  cited  above,  all,  some,  or 
none  of  S  may  be  included  in  P. 


140     TREATMENT    OF    THE    SYLLOGISM 

In  valid  syllogisms  there  may  sometimes  be  a  margin 
of  indefiniteness  (owing  to  the  indefinite  character  of 
the  "particular"  propositions),  but  a  certain  amount 
of  definite  information  regarding  the  relation  of  S  and 
P  is  always  given  and  the  relation  of  the  circles  sym- 
bolizing major  and  minor  terms  is  not  left  wholly  in 
doubt. 

The  reason  for  the  rule  requiring  the  distribution  of 
the  middle  term  may  be  stated  in  this  way:  If  each  of 
two  things  is  related  to  a  part  of  a  third,  we  can  not 
conclude  that  they  are  related  to  each  other,  for  they 
may  not  be  related  to  the  same  part;  but  if  one  (or 
both)  is  related  to  the  whole  of  the  third,  then  it  may 
be  possible  to  assert  a  relation  between  the  two.  Thus : 


All  M  is  P       No  M  is  P       All  P  is  M 

All  S  is  M       All  S  is  M       All  S  is  M 
All  S  is  P         No  S  is  P         No  conclusion. 


and  so  on 


Some  M  is  P 
All  S  is  M 
No  conclusion. 

4.  The  reason  for  rule  four  is  obvious:  if  we  know 
something  about  only  part  of  a  class  in  the  premise, 


ILLICIT    MAJOR    AND   MINOR 

we  can  not  say  something  about  all  of  it  in  the  con- 
clusion. The  violation  of  this  rule  gives  rise  to  two 
fallacies :  the  Illicit  Process  of  the  Major  Term  and  the 
Illicit  Process,  of  the  Minor  Term.  In  the  syllogism, 
"  All  men  (M)  are  vertebrates  (P)  ;  all  men  (M)  are 
rational  (S)  ;  therefore,  all  rational  beings  (S)  are 
vertebrates  (P),"  we  have  an  illustration  of  the  Illicit 
Process  of  the  Minor  Term,  or  Illicit  Minor,  as  it  is 
usually  called.  In  the  syllogism,  "  All  Chinamen  (M) 
are  Mongolians  (P)  ;  no  Japanese  (S)  are  Chinamen 
(M)  ;  therefore  no  Japanese  (S)  are  Mongolians  (P)," 
the  Illicit  Process  of  the  Major  Term  occurs.  Using 
the  circles,  we  have  for  the  first ; 


and  for  the  second: 


The  dotted  lines  indicate  possible  boundaries  of  S. 

The  premises  do  not  justify  us  in  including  all  of  S 
within  the  circle  P  in  the  first,  nor  of  excluding  all  P 
from  the  circle  S  in  the  second.  S  may  be  outside  of 
M,  but  still  be  wholly  or  partially  within  P. 

5.  With    two    negative    premises,   both   major    and 


TREATMENT    OF    THE    SYLLOGISM 

minor  terms  are  excluded  from  the  middle  term,  but 
that  does  not  tell  us  whether  they  are  or  are  not  ex- 
cluded from  each  other. 

6.  With  one  negative  premise,  either  major  or  minor 
term  is  excluded  from  the  middle  term,  while  the  other 
is  not;  therefore,  if  any  relation  can  be  asserted  be- 
tween major  and  minor  terms,  it  must  be  one  of  ex- 
clusion. 

7-8.  The  reasons  for  the  two  last  rules  can  be  more 
easily  understood  after  we  have  considered  the  Moods 
and  Figures  of  the  syllogism.  It  will  then  be  seen 
that  the  violation  of  these  rules  means  a  violation  of 
rule  three  or  rule  four  or  both. 

The  Figure  of  a  syllogism  is  determined  by  the  posi- 
tions of  the  middle  term.1 

The  Four  Figures  are  as  follows: 

1.  M  is  P   2.  P  is  M   3.  M  is  P   4.  P  is  M 
S  is  M     S  is  M     M  is  S     M  is  S 

.'.S  is  P    /.S  is  P    /.S  is  P    /.S  is  P 

In  the  First  Figure,  the  Middle  Term  is  the  subject 
of  the  Major  Premise  and  the  predicate  of  the  Minor 
Premise. 

In  the  Second  Figure  it  is  the  predicate  of  each. 

In  the  Third  Figure  it  is  the  subject  of  each. 

In  the  Fourth  Figure  it  is  the  predicate  of  the  Major 
Premise  and  the  subject  of  the  Minor  Premise. 

The  position  of  the  Middle  Term  in  the  Third  Figure 

1  We  have  already  seen  that  the  Figures  differ  in  other  ways, 
but  the  traditional  mode  of  distinguishing  them  is  the  one 
just  mentioned. 


THE    MOODS    OF    THE    SYLLOGISM 

is  the  opposite  of  that  which  it  occupies  in  the  Second ; 
and  in  the  Fourth  it  is  the  opposite  of  that  in  the  First. 
The  Mood  of  a  syllogism  is  determined  by  the  quan- 
tity and  quality  of  the  several  propositions  which  it 
contains.  Propositions,  as  we  have  seen,  are  of  four 
kinds  with  respect  to  quantity  and  quality,  and  are 
represented  by  the  four  letters,  A,  E,  I,  and  O.  The 
letters  AAA  would  symbolize  a  syllogism  in  which  each 
proposition  was  a  universal  affirmative.  There  are 
sixty- four  possible  moods : 


AAA     AT?  A     ATA     AHA       "F  A  A    T?T?  A    T?T  A    TO  A 

Xi.XXjfjL      Xl.,l_fXX     3TX  -L-TX    'Xi.x-/ZTC         ^EjiTCTTC     i_!7A-7i"3T     J-VX'XTT    "iJ7\^/XX 

-AAE-  AEE  AIB  AGE  EAE  EEE  -EIE  EGE- 
AAI  AM-  AH  -AGt  -EAI-  -EEJ-  -EH-  -EGI- 
AAG  AEG  -AJO-  AGO  EAO  EEG  EIO  EGG 

.IAA  -IEA-  KA  -IGA-  -GAA  GEA  GIA  GGA 

T  A  T>  TT^T^  TTT?  TQT^  f\  A  T?  Q'PT?  r>TT?  QQT? 
~Xi"3r£ 7  "tL  J^J^*  "A  A  "J— JT*  "A  V-/A-J"  "\_/"TA^  >V  "Vi/  J— ^"i-?  v^XX-/  vZ/VAE7 

TAT        TT?T       TTT        TOT.       O  AT      QT?T     QTT     HOT. 

JLXxJ.        "J.  JJvx"       JLJLi         '  ivyi"1        "\_/Xi.A"      "V^  J-V"3T     "Vy  i  Jtr     \y  Vx  jr 

^AG-  (IEO)-«G-    iGG-    GAG  GEG  GIG  GGG 

Many  of  these  are  at  once  seen  to  be  invalid :  thus,  ap- 
plying the  rules  for  negative  and  particular  premises, 
we  can  eliminate  those  moods  through  which  a  line  is 
drawn.  The  mood  IEO  does  not  violate  any  of  those 
rules,  but  examination  will  show  that  it  will  give  a  fal- 
lacy of  Illicit  Major  in  each  of  the  Figures.  The  con- 
clusion is  negative  and  hence  distributes  its  predicate, 
the  major  term.  The  major  premise  is  an  I  proposi- 
tion and  hence  distributes  neither  of  its  terms ;  there- 


144     TREATMENT    OF    THE    SYLLOGISM 

fore,  the  major  term  can  not  be  distributed  in  the 
premise,  and  hence  this  mood  may  be  eliminated 
also. 

There  remain  only  eleven  moods  which  may  be  valid, 
but  many  of  those  are  invalid  in  some  of  the  figures. 
We  will  examine  each  of  these  moods  in  each  of  the 
figures.2 

In  the  First  Figure  we  should  have  the  following  re- 
sults : 


A. 
A. 
A. 


-  P 


A.  @-P 


I.    S  -  P 


E. 


E.  ®x®  E.  ®x(P) 
A.  (S)-  M  A.  (S)-M 
E.  ®x©  O.  S  x© 


It  is  evident  that  the  following  are  invalid  in  the  First 
Figure:  AEE,  AEO,  AOO,  IAI,  and  OAO.  IAI  and 
OAO  are  invalid  because  of  an  Undistributed  Middle, 
the  others  because  of  Illicit  Majors. 

The  valid  moods  are  AAA,  AAI,  AH,  EAE,  EAO, 
and  EIO.  AAI  and  EAO  are  necessarily  valid  since 
AAA  and  EAE  are  valid.  I  and  O  are  called  weakened 
conclusions  because  they  are  less  general  than  they 


2  To  facilitate  dealing  with  them  we  shall  employ  the  symbols 
used  in  the  exposition  of  Conversion  and  Obversion. 


THE    SECOND    FIGURE 


145 


might  be.  A  comparison  of  these  moods  will  show  that 
two  general  statements  may  be  made  regarding  reason- 
ing in  this  figure : 

1.  The  Major  premise  must  be  universal. 

%.  The  minor  premise  must  be  affirmative, 

Examination  of  the  illustrations  given  in  the  pre- 
vious discussion  of  this  Figure  (page  127)  will  show 
that  every  syllogism  which  violated  either  of  these  two 
rules  failed  to  give  a  valid  conclusion. 

In  the  Second  Figure  the  results  are  different : 


A.  ©-  M 
O.  S  x® 
O.  Sx(P) 


A.  ©-  M 

E.  ©x® 

E.  ©x© 

E.  ©x® 
A.  ©-  M 
E.  (S)x(P) 


A.®-  M 
E.  ©x® 
O.  Sx© 

E.  ©x® 
A.  ©-  M 
O.  Sx® 


Here  the  moods,  AAA,  AAI,  AH,  IAI,  and  OAO  are 

invalid,  the  last  because  of  Illicit  Major,  the  others  be- 
cause of  Undistributed  Middle. 

The  valid  moods  are  AEE,  AEO,  AGO,  EAE,  EAO, 
and  EIO.  O  is  a  weakened  conclusion  in  AEO  and 
EAO.  Here  we  find  that  in  the  Second  Figure; 


146     TREATMENT    OF    THE    SYLLOGISM 

1.  The  major  premise  must  be  universal.  2.  One  prem- 
ise must  be  negative  and  the  conclusion  likewise  must 
be  negative. 

These  rules,  like  those  of  the  First  Figure,  might 
have  been  formulated  on  the  basis  of  the  typical  cases 
presented  in  the  earlier  discussion.  (See  p.  130.) 

Again  in  the  Third  Figure : 


A.  @-P 
I.  M-S 
I.  S  -  P 

E.  ®x(g 
I.    M  -S 
O.   Sx® 


E.  ®x(P) 
A.  ®-S 
O.   Sx(P) 


I.  M  -P 
A.  ®-S 
I.  S  -  P 


O.    Mx(P) 
A.  @-S 
O.   Sx(|) 


In  this  case  the  invalid  moods  are  AAA,  AEE,  AEO, 
AOO,  EAE.  Of  these,  AAA  and  EAE  are  cases  of 
Illicit  Minor;  and  the  rest,  of  Illicit  Majors.  The 
valid  moods  here  are  AAI,  AH,  EAO,  EIO,  IAI,  and 
OAO.  In  the  Third  Figure: 

1.  The  conclusion  must  be  particular. 

2.  The  minor  premise  must  be  affirmative. 

In  this  case,  as  in  the  others,  the  rules  might  have 
been  discovered,  without  consideration  of  the  moods,  by 
a  direct  examination  of  cases. 


THE    FOURTH    FIGURE 

In  the  Fourth  Figure  we  have: 


A.  (P)-M 
A.  @-S 
I.  S  -  P 


A.  (P)-M 
E.  ®x(S) 

o.  sx© 

E.  ©x(g 
A  ®-  S. 
O.  SxfP) 


Here  the  invalid  moods  are  AAA,  AH,  AGO,  EAE,  and 
OAO.  AAA  and  EAE  give  Illicit  Minor,  AH  and  AGO 
give  Undistributed  Middle,  and  OAO  gives  Illicit  Ma- 
jor. The  valid  moods  are  AAI,  AEE,  AEO,  EIO,  IAL 
We  get  these  rules  for  the  Fourth  Figure : 

1.  If   the  major  premise  be  affirmative,    the  minor 
premise  must  be  universal. 

2.  If  the  major  premise  be  also  particular,  the  minor 
premise  must  be  affirmative. 

3.  //  the  minor  premise  be  affirmative,  the  conclusion 
must  be  particular. 

4.  //  either  premise  be  negative,  the  major  must  be 
universal. 

5.  The  conclusion  may  not  be  a  universal  affirmative 
proposition. 


148     TREATMENT    OF    THE    SYLLOGISM 

Comparison  of  all  the  valid  moods  shows  that  the 
mood  AAA  is  valid  in  the  First  Figure  only.  As  this 
is  the  only  mood  in  which  A  appears  as  a  valid  con- 
clusion, it  will  be  evident  that  a  universal  affirmative 
conclusion  can  be  proved  in  the  First  Figure  only. 

REDUCTION    OF    THE    MOODS    AND    FIGURES. 

The  Medieval  schoolmen  invented  a  set  of  menemonic  verses 
to  serve  as  an  aid  to  the  memory  in  recalling  the  valid  modes  in 
the  several  Figures.  The  verses  consisted  of  barbarous  Latin 
terms.  The  words  contain  also  letters  for  guidance  in  reduction 
of  the  other  Figures  into  the  First.  These  verses,  with  their 
interpretation,  are  as  follows: 

Barbara,  Celarent,  Dam,  Fenoque  prioris; 
Cesare,  Camestres  Festino,  Baroko  secundae; 
Tertia,  Darapti,  Disarms,  Datisi,  Felapton, 
Bokardo,   Fm'son,  habet,  quarta  insuper  addit 
Bramanttp,  Camenes;   Dimaris,   Fesapo,   Fresison. 

The  moods  are  indicated  by  the  italicised  letters.  All  the 
valid  moods  are  included  except  those  in  which  there  are  so- 
called  weakened  conclusions,  i.  e.,  cases  in  which  a  particular 
conclusion  is  drawn,  though  a  universal  would  be  valid,  such  as 
AAI  or  EAO  in  the  First  Figure.  The  first  line  indicates  the 
moods  of  the  First  Figure,  the  second  line,  of  the  Second,  the 
third  and  the  first  half  of  the  fourth  indicate  those  of  the 
Third  Figure,  and  the  last  line,  those  of  the  Fourth  Figure. 

The  First  Figure  was  regarded  as  the  Perfect  Figure,  and  the 
others  were  transformed  into  it  by  making  certain  changes  in 
their  various  members.  This  process  was  called  the  Reduction 
of  the  Imperfect  Figures.  These  words  contain  letters  which 
stand  for  the  changes  which  must  be  made.  The  capital  letters 
in  the  last  four  lines  indicate  the  mood  of  the  First  Figure  to 
which  the  mood,  indicated  by  the  word  in  which  they  are  found, 
may  be  reduced.  Thus  Cesare  may  be  reduced  to  Celarent. 
p  indicates  that  the  preceding  proposition  is  to  be  converted 
per  accidens  or  by  limitation;  s  indicates  that  the  preceding 
proposition  is  to  be  converted  simply,  and  m  indicates  that  the 
premises  are  to  be  transposed. 

CAMESTRES  CELARENT 

AH  A  is  C  C  is  not  B 

(All  stars  are  suns)  (No   suns   are  planets) 

No  B  is  C  All  A  is  C 

(No  planets  are  suns)  (All    stars    are    suns) 

Therefore,  B  is  not  A  Therefore,  no  A  is  B. 

(No  planets  are  stars)  (No  stars  are  planets) 


REDUCTION   OF    THE    FIGURES        149 

The  minor  premise  in  Camestres  is  first  converted,  then  the 
two  premises  are  transposed,  and  finally  the  conclusion  is  con- 
verted. To  reduce  Cesare  to  Celarent  we  need  only  convert 
the  major  premise. 

As  a  second  example  we  may  take  the  reduction  of  Bramantip 
to  Barbara. 

BRAMANTIP  BARBARA 

All  C  is    B  All  B  is  A 

All  B  is  A  All  C  is   B 

Some   A   is   C  All  C  is  A 

In  this  case,  the  premises  are  transposed,  and  the  conclusion 
is  converted.  This  would  give  AAI.  But  the  conclusion  A  would 
be  valid  from  these  premises.  The  p  in  this  case  may  be  taken 
as  indicating  that,  instead  of  a  conclusion  less  in  quantity  than 
the  original  proposition,  we  may  have  one  which  is  greater  in 
quantity,  namely,  universal. 

There  is  one  more  significant  letter  in  these  words,  the  letter 
k.  It  indicates  that  the  reduction  must  be  made  by  indirect 
means.  Take,  for  example,  Bokardo  which  reduces  to  Bar- 
bara. 

BOKARDO  BARBARA 

Some  A  is  not  C  All  B   is  C 

All  A  is  B  All  A  is  B 

Therefore,  some  B  is  not  C  Therefore,  all  A  is  C 

In  this  case  the  major  premise  of  Bokardo  is  the  contradictory 
of  the  conclusion  of  Barbara;  and  the  conclusion  of  Bokardo 
is  the  contradictory  of  the  major  premise  of  Barbara.  Suppose 
the  conclusion  of  Bokardo  to  be  false ;  then  its  contradictory,  "  All 
B  is  C,"  will  be  true;  taking  this  as  the  major  premise  of  a  new 
syllogism  and  the  proposition,  "  all  A  is  B,"  as  the  minor  pre- 
mise, the  conclusion  will  be  the  contradictory  of  the  major  premise 
of  Bokardo  and  the  new  syllogism  will  be  in  the  mood  Barbara. 
Bokardo  may  be  also  be  reduced  to  Darii.  First  obvert,  then  con- 
vert, the  major  premise;  transposing  the  two  premises,  we  then 
have  Darii.  All  this  mechanism  is  entirely  unscientific  and  its 
interest  is  purely  historical. 

EXERCISES    ON    THE    SYLLOGISM 

1.  What  kinds  of  propositions  are  incapable  of  proof  in 
the  Second,  Third  and  Fourth  Figures  respectively?     Give 
the  reasons  for  your  reply. 

2.  If  either  premise  of  a  syllogism  is  O,  what  must  the 
other  be? 

3.  With  I  as  the  major  premise,  what  must  the  minor 
premise  be? 


150     TREATMENT    OF    THE    SYLLOGISM 

4.  Show  that  an  E   proposition  is   highly  efficient  as   a 
major  premise.  (J.)s 

5.  Show  that  O  is  seldom  admissible  as  a  minor  premise. 

(j.) 

6.  Prove  that  there  must  always  be  in  the  premises  one 
more  distributed  term  than  in  the  conclusion.     (J.) 

7.  Prove  from  the  general  rules  of  the  syllogism,  that 
when  the  major  term  is  the  predicate  in  its  premise,  the 
minor  premise  must  be  affirmative.     (J.) 

8.  Point  out  which  of  the  following  pairs  of  premises 
will   give  a  syllogistic   conclusion,  and  name  the  obstacle 
which  exists  in  other  cases. 

(1)  No  A  is  B;  some  B  is  not  C. 

(2)  No  A  is  B;  some  not  C  is  B. 

(3)  All  B  is  not  A;  some  not  A  is  B. 

(4)  Some  not  A  is  B;  no  C  is  B. 

(5)  All  not  B  is  C;  some  not  A  is  B. 

(6)  All  A  is  B;  all  not  C  is  B. 

(7)  All  not  B  is  not  C;  all  not  A  is  not  B. 

(8)  All  A  is  not  B;  no  B  is  C. 

(9)  All  C  is  not  B ;  no  A  is  not  B. 

3  (J)  refers  to  Jevons,  Studies  in  Deductive  Logic,  where 
a  great  many  more  questions  of  this  character  may  be  found 
The  following  exercise  is  from  the  same  source. 


CHAPTER    X 

ABBREVIATED    AND    COMPLEX    FORMS    OF 

REASONING  -  -  HYPOTHETICAL  AND 

DISJUNCTIVE    SYLLOGISMS 

The  Enthymeme. — Usually  our  reasoning  does  not 
fall  into  the  form  of  a  perfect  syllogism.  In  the  first 
place  it  very  often  happens  that  one  or  another  of  the 
propositions  is  omitted.  For  example,  "  This  object 
can  be  magnetized,  for  it  is  made  of  iron,"  omits  the 
major  premise,  "  All  things  made  of  iron  can  be  mag- 
netized." Again,  in  "  Every  member  of  the  jury  voted 
for  acquittal,  therefore  X  voted  for  acquittal,"  the 
minor  premise,  "  X  was  a  member  of  the  jury,"  is 
omitted.  In  "  All  metals  are  elements ;  this  is  a  metal," 
the  conclusion  is  omitted. 

Syllogisms  from  which  one  proposition  is  missing  are 
called  Enthymemes.  The  missing  premise  can  usually 
be  found  without  difficulty.  The  two  propositions  which 
are  given  contain  the  three  terms  of  the  syllogism ;  one 
of  these  will  be  common  to  the  two  propositions,  and  the 
missing  proposition  will  contain  the  other  two  terms. 
Thus  with  the  proposition,  "  S  is  M ;  hence,  S  is  P," 
the  missing  premise  is  clearly  "  M  is  P,"  or  "  P  is  M." 
With  "  M  is  P ;  therefore,  S  is  P,"  the  missing  premise 
will  contain  S  and  M. 

The  danger  of  false  reasoning  is  greater  here  than 
in  the  complete  syllogism,  since  the  proposition  which 
is  not  expressed  may  be  false  or  inadequate,  and  if  the 

151 


152          HYPOTHETICAL    SYLLOGISMS 

proposition  is  not  definitely  stated  its  inadequacy  is 
easily  overlooked. 

The  Enthymeme  is  an  incomplete  form  of  syllogistic 
reasoning ;  it  is  less  than  a  syllogism.  There  are  several 
complex  forms  in  which  we  find  more  than  a  syllogism. 

PROSYLLOGISM  AND  EPISYLLOGISM. — Two  complete 
syllogisms  may  be  united  by  having  a  proposition  in 
common.  Thus : 

r  All  the  Romance  languages  are  derived  from 

Prosyllogism  J  vLatl,n;. 

rrench  is  a  Romance  language; 

^-Therefore,   French  is   derived   from   Latin, 
f  This  man  speaks  French; 

Episyllogism  J  Therefore,  this  man  speaks  a  language  de- 
{      rived  from  Latin. 

In  this  example  the  conclusion  of  the  first  syllogism 
is  the  major  premise  of  the  second.  This  is  known  as 
Prosyllogism  and  Episyllogism,  the  conclusion  of  the 
Prosyllogism  being  the  major  premise  of  the  Episyllo- 
gism. One  syllogism  might,  of  course,  establish  the 
minor  premise  of  the  other: 

f  French  is  a  Romance  language; 
J  This  man  speaks  French. 
1  ]  Therefore,  this  man  speaks  a  Romance  larr- 
[      guage. 
f  All  the  Romance  languages  are  derived  from 

Episyllogism  J  rrLatin;i  . 

I  Hence,  this  man  speaks  a  language  derived 

[      from  Latin, 

Again,  it  might  have  each  of  its  premises  established 
by  another  syllogism: 


PROSYLLOGISM    AND    EPISYLLOGISM     153 

Everything  which  is  able  to  restrain  trade 

is  a  source  of  danger; 
Prosyllogism  ^  Every  monopoly  is  able  to  restrain  trade; 

Hence,    every    monopoly    is    a    source    of 

danger. 

A  company  which  has  complete  control  of 

a  certain  commodity  is  a  monopoly; 

Prosyllogism^   This   trust  has  complete  control  of   a  cer- 
tain commodity; 
Hence,  this  trust  is  a  monopoly. 
Conclusion:     Therefore,    this    trust    is    a 
source  of  danger. 


An  enthymeme  might  take  the  place  of  the  complete 
syllogism  in  the  case  of  either  or  both  of  the  prosyllo- 
gisms.  Further,  the  premises  of  the  prosyllogisms 
might  themselves  be  supported  by  other  syllogisms. 

A  great  many  syllogisms  may  be  combined  into  one 
reasoning  process,  and  most  reasoning  processes  con- 
tain several  syllogisms,  complete  or  abbreviated.1 

i  Geometrical  reasoning  illustrates  abbreviated  reasoning  very 
clearly.  For  example  take  the  proof  of  the  proposition  that  "  All 
straight  angles  are  equal." 


A S B 

D I F 


"Let  the  angles  ACB  and  DEF  be  any  two  straight  angles. 
To  prove  that  the  angle  ACB  equals  the  angle  DEF. 

"  Place  the  angle  ACB  on  the  angle  DEF,  so  that  the  vertex  C 
shall  fall  on  the  vertex  E,  and  the  side  CB  on  the  side  EF.  Then 
CA  will  fall  on  ED.  Therefore  the  angle  ACB  equals  the  angle 
DEF."  (Wentworth,  Plane  Geometry,  page  14.) 

This  is  the  proof  in  an  abbreviated  form.  It  might  be  more 
fully  expressed  as  follows:  (See  page  154.) 


154          HYPOTHETICAL    SYLLOGISMS 

We  might  have  a  chain  of  syllogisms  in  which  the 
conclusion  of  each  was  the  minor  premise  of  the  one 
following. 

All  ungulates  are  mammals. 
All  mammals  are  warm-blooded. 
All  ungulates  are  warm-blooded. 

All  warm-blooded  animals  have  lungs. 
All   ungulates   are  warm-blooded   animals. 
All  ungulates  have  lungs. 

All  animals  that  have  lungs  require  air. 
All  ungulates  have  lungs. 
All  ungulates  require  air. 


"  What  is  true  of  the  angles  ACB  and  DEF  will  be  true  of  all 
straight  angles. 

Two  angles  which  can  be  so  placed  upon  each  other  that 
their  vertices  coincide  and  their  sides  coincide  are 
equal,  each  with  the  other. 

(  Any  figure  may  be  moved  from  one  place  to  another 
)        without   altering  its  shape.    (Axiom  of  superposi- 
j       tion.)      Therefore,  the  figure  ACB  may  be  placed 
upon  the  figure  DEF  without  altering  its  shape. 
Straight  angles  are  such  as  have  their  sides  ex- 
tending in  opposite  directions   so  as  to  be  in 
the  same  straight  line.     Th'e  angles  ACB  and 
DEF  have  their  sides  so  extending.     Hence 
the  lines  AB  and  EF  are  straight  lines. 

Two  straight  lines  which  have  two 
points  in  common  coincide  and 
and  form  but  one  line. 
When  the  figure  ACB  is  super- 
posed on  the  figure  DEF  so  that 
the  vertex  C  shall  fall  on  the  ver- 
tex E,  and  the  side  CB  on  the 
side  EF,  the  straight  line  AB 
falls  on  the  straight  line  DF  and 
they  coincide;  the  line  CA  falls 
on  the  line  ED,  and  coincides 
with  it,  CB  coincides  with  EF, 
[And  C  coincides  with  E]. 

|^  Therefore  the  angle  ACB  and  the  angle  DEF  are  equal. 
Therefore  all  straight  angles  are  equal. 
Geometrical  reasoning   is    not    all   syllogistic    in    the   narrowest 
sense  of  the  word.     See  chapter  xvii. 


THE    SORITES  155 

THE  SORITES. — Now,  instead  of  putting  the  conclu- 
sion in  words  and  repeating  it  in  the  succeeding  propo- 
sition, we  may  omit  everything  except  the  new  premises 
until  we  are  ready  to  draw  the  final  conclusion.  Thus : 

All  ungulates  are  mammals.  A  is  B 

All  mammals   are  warm-blooded.  B  is  C 

All  warm-blooded  animals  have  lungs.     C  is  D 
All  animals  that  have  lungs  require  air.  D  is  E 
Hence,  All  ungulates  require  air.  A  is  E. 

This  is  known  as  the  Sorites;  a  Sorites  may  have  any 
number  of  members.  There  are  two  forms.  That  given 
above,  is  an  example  of  the  Progressive  or  Aristotelian 
Sorites.  The  premise  containing  the  subject  of  the 
conclusion  (the  Final  Minor)  comes  first  in  order;  that 
containing  its  predicate  (The  Prime  Major)  comes 
last;  the  intermediate  propositions  serve  to  connect  the 
two.  In  the  Regressive  or  Goclenian  Sorites,  the  Prime 
Major  comes  first  and  the  Final  Minor  last  among  the 
premises.  If  expanded  into  a  chain  of  prosyllogisms 
and  episyllogisms,  the  conclusion  of  each  syllogism 
would  be  the  major  premise  of  the  one  following.  For 
example : 

A  European  is  a  Caucasian.  B  is  A 
A  Frenchman  is  a  European.  C  is  B 
A  Parisian  is  a  Frenchman.  D  is  C 

This   author   is   a   Parisian.  E  is  D 

Hence,    This   author  is  a  Caucasian.         E  is  A 

In  both  forms  of  the  sorites  the  reasoning  is  in  the 
first  figure  of  the  syllogism.  With  the  exception  of 
the  terms  which  are  contained  in  the  conclusion,  every 
term  in  the  sorites  is  a  middle  term.  The  greatest 
source  of  danger  in  this  form  of  reasoning  is  to  be 
found  in  ambiguous  terms. 


156          HYPOTHETICAL    SYLLOGISMS 

Only  the  Final  Minor  premise  may  be  particular; 
only  the  Prime  Major  may  be  negative. 

Hypothetical  Reasoning. — The  forms  of  reasoning 
with  which  we  have  been  dealing  in  the  last  three  chap- 
ters have  employed  only  declarative  sentences,  or  Cate- 
gorical Propositions,  as  they  are  called  in  Logic.  A 
categorical  proposition  is  an  unconditional  statement. 
"  A  is  B  "  or  "  A  is  not  B  "  are  typical  forms.  But 
there  are  other  kinds  of  propositions ;  one  of  these  is 
the  Hypothetical  Proposition.  A  hypothetical  prop- 
osition is  one  containing  a  categorical  proposition  and 
the  statement  of  a  condition  on  which  the  truth  of  the 
categorical  depends.  The  conditional  member  of  the 
proposition  is  .called  the  Antecedent;  the  categorical 
member  is  called  the  Consequent.  A  hypothetical  propo- 
sition may  be  made  the  major  premise  of  a  syllogism. 

Such  a  syllogism  would  be  a  HYPOTHETICAL  SYLLO- 
GISM. The  Hypothetical  syllogism  has  four  forms. 

1.  If  A  is  B,  C  is  D.     If  the  substance  is  carbon,  it  will 

burn. 

A  is  B  It  is  carbon. 

.*.  C  is  D  .'.It  will  burn. 

2.  If  A  is  B,  C  is  D.     If  the  substance  is  carbon,  it  will 

burn. 

A  is  not  B  It  is  not  carbon. 

.*.  C  is  not  D  .'.It  will  not  burn. 

3.  If  A  is  B,  C  is  D.     If  the  substance  is  carbon,  it  will 

burn. 

C  is  D  It  will  burn. 

.'.A  is  B  .'.It  is  carbon. 

4.  If  A  is  B,  C  is  D.     If  the  substance  is  carbon,  it  will 

burn. 

C  is  not  D  It  will  irot  burn. 

.'.A  is  not  B  .".It  is  not  carbon. 


THE    HYPOTHETICAL    SYLLOGISM     157 

The  first  of  these  affirms  the  antecedent,  the  second 
denies  it;  the  third  affirms  the  consequent,  and  the 
fourth  denies  it.  The  second  and  third  are  obviously 
invalid.  The  fact  that  the  substance  is  not  carbon 
gives  us  no  further  information  about  qualities  ;  and  the 
fact  that  it  will  burn  does  not  insure  its  being  carbon. 
These  instances  are  typical  and  illustrate  the  general 
rule  that  Denying  the  antecedent  or  affirming  the  conse- 
quent in  a  hypothetical  syllogism  are  invalid  forms  of 
reasoning.2 

We  may  have  a  hypothetical  syllogism  in  which  the 
minor  premise  is  also  a  hypothetical  proposition. 

If  A  is  B,  C  is  D.         If  he  is  nominated,  he  will  be 

elected. 

If  C  is  D,  E  is  F.         If   he   is   elected,  this   measure 

will  not  pass. 

.'.If  A  is  B,  E  is  F.       .'.If  he  is  nominated,  this  meas- 
ure will  not  pass. 

Disjunctive  Reasoning. —  There  is  a  third  kind  of 
so-called  syllogism  with  still  another  sort  of  proposi- 
tion as  its  major  premise.  This  is  the  Disjunctive 
Syllogism  and  its  major  premise  is  a  Disjunctive  Prop- 
osition. A  disjunctive  proposition  is  one  which  states 
an  alternative.  "  A  is  either  B  or  C  " ;  "  It  will  either 
rain  or  snow."  The  minor  premise  either  affirms  or 

2  There  are  cases,  however,  in  which  these  forms  give  true 
conclusions.  If  the  antecedent  is  the  only  one  on  which  the  con- 
sequent would  follow  then  all  the  forms  of  the  hypothetical  syllo- 
gism would  give  valid  conclusions.  For  example,  if  we  had  the 
major  premise,  "  If  A  is  B,  and  in  no  other  case,  C  will  be  D," 
then  to  deny  that  A  is  B  would  necessitate  the  conclusion  that  C 
is  not  D.  We  may  take,  as  a  concrete  case,  "  If  a  triangle  is 
equilateral,  and  in  no  other  circumstances,  it  will  be  equiangular. 
This  triangle  is  not  equiangular;  hence  it  is  not  equilateral";  or, 
"  This  triangle  is  equilateral,  therefore  it  is  equiangular,"  and 
so  on. 


158          HYPOTHETICAL    SYLLOGISMS 

denies  one  of  the  alternatives.     The  conclusion  either 
denies  or  affirms  the  other. 

A  is  either  B  or  C  It  will   either   rain  or  snow. 

A  is  B  It  will  rain. 

/.A  is  not  C  .'.It  will  not  snow. 

A  is  either  B  or  C  It  will   either   rain  or  snow. 

A  is  C  It  will  snow. 

/.A  is  not  B  .".It  will  not  rain. 

A  is  either  B  or  C  It  will   either   rain  or  snow. 

A  is  rrot  B  It  will  not  rain. 

.'.A  is  C  /.It  will  snow. 

A  is  either  B  or  C  It  will   either   rain  or  snow. 

A  is  not  C  It  will  not  snow. 

,*.A  is  B  /.It  will  rain. 

All  these  forms  are  valid.  The  only  source  of  danger 
is  in  the  major  premise.  If  the  alternatives  are  not 
true  alternatives,  the  conclusion  can  not  be  trusted.  If 
A  can  be  anything  else  than  B  or  C,  or  if  it  can  be  both 
at  the  same  time,  the  denial  or  affirmation  of  one  alter- 
native cannot  assure  us  of  the  truth  or  falsity  of  the 
others. 

There  are  more  -complex  forms  of  disjunctive  reason- 
ing ;  we  might,  for  example,  have  the  proposition,  "  A 
is  B  or  C  or  D,  etc."  In  this  case  the  affirmation  of  one 
would  mean  the  denial  of  the  other  two ;  but  the  de- 
nial of  one  would  give  as  the  conclusion  a  disjunctive 
proposition  containing  the  two  others  as  alternatives. 
Thus  "  A  is  not  B ;  A  is  either  C  or  D,  etc."  Similarly 
the  assertion  "  A  is  B  or  C  "  would  give  the  conclusion 
"  A  is  not  D,  etc.,"  and  so  on. 


THE    DILEMMA  159 

There  are  certain  imperfect  forms  of  this  syllogism 
which  are  sometimes  useful.  Sometimes  we  know  that 
A  is  B  or  C  or,  it  may  be,  both.  In  such  a  case,  if  we 
know  that  A  is  not  B,  then  it  must  be  C,  but  if  we  know 
that  it  is  B,  we  do  not  know  that  it  is  not  also  C.  With 
such  a  major  premise,  the  minor  premises  which  are 
affirmative  do  not  give  valid  -conclusions.  It  would  be 
simpler  in  such  cases  to  state  the  three  possibilities  as 
mutually  exclusive,  "  A  is  B  or  C,  or  both  B  and  C,"  and 
proceed  as  in  the  perfect  forms  of  the  hypothetical 
syllogism. 

More  Complex  Forms.  THE  DILEMMA. — There  are 
more  complex  forms  of  reasoning  in  which  hypothetical 
and  disjunctive  propositions  are  combined.  Thus  we 
may  have: 

If  A  is  B,  C  is  D  or  E   (or  C  is  D  or  E  is  F). 
A  is  B.  .'.  C  is  D  or  E   (or  C  is  D  or  E  is  F). 

More  concretely : 

If  he  fails,  he  will  leave  college  or  drop  back  a  class. 
But  he  is  sure  to  fail. 
.".  He  will  leave  college  or  drop  back  a  class. 

If  the  antecedent  were  denied  there  could  be  no  valid 
conclusion ;  in  this  and  all  other  respects  this  syllogism 
is  like  a  simple  hypothetical  syllogism  except  in  having 
a  disjunctive  consequent,  instead  of  a  categorical  one. 
We  get  more  complicated  forms  when  the  major  pre- 
mise consists  of  two  hypothetical  propositions,  in  which 
either  the  antecedents  or  the  consequents  are  found  to 


160          HYPOTHETICAL    SYLLOGISMS 

be  alternative:  the  minor  premise  is  a  disjunctive 
proposition,  and  the  resulting  syllogism  is  a  Di- 
lemma. 

If  A  is  B,  C  is  D;  aiid  if  E  is  F,  C  is  D. 
But  either  A  is  B  or  E  is  F. 
.'.  C  is  D. 

If  a  college  education  gives  a  student  useful  information, 
it  is  valuable  to  him. 

If  it  gives  him  mental  training  it  is  valuable  to  him. 

But  it  either  gives  him  useful  information  or  mental 
training. 

.'.It  is  valuable  to  him. 

This  is  a  Simple  Constructive  Dilemma:  simple  be- 
cause the  consequents  of  the  hypothetical  propositions 
in  the  major  premise  are  the  same  in  both  cases;  con- 
structive because  it  establishes  an  affirmative  conclu- 
sion. 

If  the  consequents  were  denied  we  should  not  have  a 
dilemma,  but  two  simple  hypothetical  syllogisms.  There 
would  be  no  disjunctive  premise. 

The  second  form  of  the  dilemma  is  the  Complex  Con- 
structive  Dilemma.  In  this,  the  consequents  of  the 
hypothetical  propositions  in  the  major  premise  are  not 
the  same. 

If  A  is  B,  C  is  D ;  and  if  E  is  F,  G  is  H. 
But  either  A  is  B  or  E  is  F. 
.'.  Either  C  is  D,  or  G  is  H. 

"  If  a  statesman  who  sees  his  former  opinions  to  be 
wrong  does  not  alter  his  course  he  is  guilty  of  deceit;  and 
if  he  does  alter  his  course  he  is  open  to  a  charge  of  incon- 
sistency; but  either  he  does  not  alter  his  course  or  he  does; 
therefore,  he  is  either  guilty  of  deceit,  or  he  is  open  to  a 
charge  of  inconsistency."  (Jevons,  Lessons  in  Logic,  p. 
168.) 


THE    DILEMMA  161 

Unlike  the  simple  dilemma,  this  has  a  disjunctive 
conclusion. 

The  Complex  Destructive  Dilemma  has  a  negative 
minor  premise  and  a  negative  -conclusion, 

If  A  is  B,  C  is  D;  and  if  E  is  F,  G  is  H. 
But  either  C  is  not  D  or  G  is  not  H. 
.".  Either  A  is  not  B  or  E  is  not  F. 

"If  this  man  were  wise,  he  would  not  speak  irreverently 
of  the  Scripture  in  jest;  and  if  he  were  good  he  would  not 
do  so  in  earnest;  but  he  does  it  either  in  jest  or  in  earnest; 
therefore,  he  is  either  not  wise,  or  not  good.  (Whately, 
Elements  of  Logic.) 

If  the  minor  premise  were  "  Neither  C  is  D  nor  G  is 
H  "  we  should  not  have  a  dilemma.  The  minor  premise 
would  not  be  disjunctive  and  we  should  have  two  simple 
hypothetical  syllogisms. 

Asserting  that  one  or  the  other  of  the  antecedents 
was  false,  or  that  one  or  the  other  of  the  consequents 
was  true  would  be  fallacious,  as  in  the  case  of  the  simple 
hypothetical  syllogism. 

In  practice  it  is  very  difficult  to  find  true  major 
premises  for  a  dilemma.  Moreover,  "  a  dilemma  can 
often  be  retorted  by  producing  as  cogent  a  dilemma  to 
a  contrary  effect.  Thus  an  Athenian  mother,  accord- 
ing to  Aristotle,  addressed  her  son  in  the  following 
words :  "  Do  not  enter  into  public  business  ;  for  if  you 
say  what  is  just,  men  will  hate  you;  and  if  you  say 
what  is  unjust,  the  gods  will  hate  you."  To  which 
Aristotle  suggests  the  following  retort :  "  I  ought  to 
enter  into  public  affairs ;  for  if  I  say  what  is  just,  the 
gods  will  love  me;  and  if  I  say  what  is  unjust,  men 
will  love  me."  (Jevons.) 


162          HYPOTHETICAL    SYLLOGISMS 

The  conclusion  of  a  dilemma,  as  of  any  other  form 
of  reasoning,  may  serve  as  a  premise  for  further  rea- 
soning. 

Extra-syllogistic  Reasoning. — Certain  other  forms 
of  reasoning  call  for  some  discussion  here.  They  are 
not  syllogistic,  but  they  are  closely  related  to  syllo- 
gistic reasoning.  For  example,  "  A  is  taller  than  B ; 
B  is  taller  than  C ;  therefore  A  is  taller  than  C."  This 
is  not  a  syllogism.  There  are  five  terms  in  the  reason- 
ing; A,  B,  C,  taller  than  B,  and  taller  than  C.  There 
is  a  similar  difficulty  in  this :  "  M  is  east  of  N ;  N  is 
east  of  O,  therefore  M  is  east  of  O."  It  would,  of 
course,  be  possible  to  construct  a  syllogism  which  would 
cover  the  ground  in  each  of  these  -cases.  Thus,  "  What- 
ever is  taller  than  another  thing  is  taller  than  every- 
thing which  is  shorter  than  that  thing;  A,  B,  and  C 
present  a  case,  etc."  And  similarly  in  the  other  example. 
Some  such  principles  as  these  are  implied,  but  the  rea- 
soning as  stated  is  not  in  the  form  of  a  simple  syllo- 
gism. We  have  here  a  system  of  relations  which  is  more 
complicated  than  that  found  in  the  ordinary  syllogism. 
In  the  latter  we  need  have  only  our  premises  and  the 
ordinary  laws  of  reasoning,  to  assure  our  conclusion ; 
in  reasoning  of  the  sort  illustrated  in  these  examples 
we  must  have,  besides  our  premises,  a  supply  of  in- 
formation about  the  general  system  of  things  to  which 
the  data  in  question  belong.  When  such  reasoning  is 
thrown  into  the  syllogistic  form  the  major  premise 
states  the  main  principles  of  the  system,  as  in  the  ex- 
ample above.  Sometimes  our  information  about  the  sys- 
tem would  be  sufficient  to  warrant  a  conclusion  and 
sometimes  it  would  not;  sometimes  the  fact  that  two 


EXTRA-SYLLOGISTIC    REASONING      163 

things  are  related  to  a  third  gives  us  information  re- 
garding their  relations  to  each  other  and  sometimes  it 
does  not.  From  the  statements  that  "  A  is  the  employer 
or  friend  or  enemy  of  B  "  and  that  "  B  is  the  em- 
ployer or  friend  or  enemy  of  C,"  we  could  not  draw 
any  conclusion  with  regard  to  A's  direct  relations  to 
C.  Things  equal  to  the  same  thing  are  equal  to  each 
other,  but  it  is  not  necessarily  true  that  things  unequal 
to  the  same  thing  will  be  unequal  to  each  other.  In 
the  latter  case  there  are  two  possibilities ;  the  system 
is  not  clearly  enough  defined  to  make  certain  any  con- 
clusion at  all.  This  was  true  in  some  of  the  illustra- 
tions given  above.  To  decide  in  any  given  case  we  must 
first  determine  whether  the  set  of  relations  involved  is 
completely  enough  known  to  justify  a  conclusion;  in 
other  words,  Is  more  than  one  conclusion  possible? 
Sometimes  the  system  may  be  very  complex,  but  its  parts 
may  be  so  related  to  each  other  and  so  -completely 
known  as  to  make  a  conclusion  possible.  A  conclusion 
may  simply  state  the  relation  of  the  terms  in  a  reverse 
order.  "  A  is  east  of  B,  therefore  B  is  west  of  A."  The' 
conclusion  may  represent  a  pathway  through  a  system 
from  one  particular  part  to  another ;  while  the  premise 
may  be  merely  the  same  pathway  followed  from  the 
other  end.  If  A  is  the  son-in-law  of  the  half-sister  of 
B's  grandfather,  then  B  is  the  grandson  of  the  half- 
brother  of  A's  mother-in-law.  The  system  might  have 
any  degree  of  complication  whatever,  but  if  the  several 
relations  could  be  read  from  either  end  the  pathway 
could  jpe  followed  in  either  direction.  Reasoning  of 
this  sort  might  be  regarded  as  a  broader  form  of  con- 
sion.3 
See  Aikins,  Principles  of  Logic,  chap.  xi. 


164          HYPOTHETICAL    SYLLOGISMS 


EXERCISES. 

1.  Supply  the  missing  proposition's  in  the  following: 

(1)  He    is    a    politician    and    therefore    not   to   be 

trusted. 

(2)  They  were  all  brave  men  and  this  man  was  one 

of  them. 

(3)  Whales  have  warm  blood  but  fish  do  not. 

(4)  Only  members  will  be  admitted;  that  excludes 

you. 

2.  Determine  which  of  the  following  give  valid  conclu- 
sions and  which  do  not;  point  out  the  fallacies  involved: 

(1)  If  he  goes,  I  shall  remain;  but  he  will  not  go. 

(2)  If  he  goes,  I  shall  remain;  and  I  shall  remain. 

main. 

(3)  I  shall  remain  if  he  goes;  and  he  will  go. 

(4)  If  it  rains  to-morrow,  the  game  will  be  post- 

poned; the  game  will  be  postponed. 

(5)  If  all  the  sides  of  this  triangle  are  equal  its 

angles  are  equal  too;  now  its  angles  are  not 
equal. 

(6)  If  he  fails  it  will  be  because  he  has  not  worked 

hard ;  and  he  has  not  worked  hard. 

3.  Criticise  the  following,  stating  the  form  of  reasoning 
in  each  case: 

(1)  A   great   man   must   either   have   extraordinary 

natural  ability  or  exceptional  capacity  for 
work;  this  man  had  extraordinary  natural 
ability,  hence  we  may  assume  that  his  capacity 
or  work  was  rrot  unusual. 

(2)  If  the  government  enacts  such  a  law  it  must 

either  adopt  socialism  or  go  into  bankruptcy; 
but  it  will  not  enact  such  a  law;  so  there  is  iro 
danger  of  either  socialism  or  bankruptcy. — 
(Hyslop.) 

(3)  If   capital   punishment   involves   cruelty   to   its 

victims  it  ought  to  be  abolished  in  favor  of 
some  other  permlty;  if  it  does  no  good  for  so- 
ciety it  should  also  be  abolished.  But  either 
it  involves  cruelty  to  its  victims  or  it  does  no 


EXERCISES  165 

good  to  society,  and  hence  it  ought  to  be  abol- 
ished.— (Hyslop.) 

(4)  If  he  sinks  he  will  be  drowned,  and  if  he  swims 

he  will  be  captured  by  the  enemy;  but  he  must 
either  sink  or  swim;  therefore,  he  will  either 
be  drowned  or  captured  by  the  enemy. 

(5)  If  he  tells  the  truth  he  will  be  forgiven,  and 

if  he  does  not  he  will  escape  detection;  but 
either  he  will  be  forgiven  or  he  will  escape 
detection;  hence  he  will  either  tell  the  truth 
or  he  will  not. 

(6)  If  he  did  that  intentionally  he  is  not  wise,  and 

if  he  did  it  unintentionally  he  is  not  lucky; 
but  he  is  neither  wise  nor  lucky;  therefore,  he 
did   it   neither   intentionally   nor   unintention- 
ally. 
4.  In  a  sorites  why  must  all  the   premises   except  the 

prime  major  be  affirmative  and  all  except  the  final  minor 

be  universal? 


CHAPTER    XI 

I.  PROOF    AND    DISPROOF.     II.  FAILURE    TO 
PROVE 

I.  Various  Kinds  of  Proof. — The  conclusion  of  a 
valid  syllogism  is  proved;  and  so  also  is  the  conclusion 
of  each  of  the  other  forms  of  reasoning  which  we  have 
examined.  A  proposition  is  proved  when  it  is  shown 
to  be  the  necessary  consequence  of  any  combination  of 
admitted  propositions.  All  the  cases  which  we  have  so 
.far  examined  are  instances  of  direct  proof.  In  direct 
proof  we  show  that,  granted  certain  things,  the  con- 
clusion necessarily  follows.  A  conclusion  is  proved  only 
when  it  is  shown  that  the  conclusion  must  be  true. 

There  are  several  other  kinds  of  proof ;  in  this  chap- 
ter we  shall  consider  the  other  kinds,  and  also  the  va- 
rious forms  of  failure  to  prove,  or  fallacy. 

INDIRECT  PROOF. — The  first  to  be  considered  is 
indirect  proof ;  we  prove  a  proposition  indirectly  by  dis- 
proving its  contradictory,  i.  e.,  by  showing  that  its  con- 
tradictory cannot  be  true. 

To  disprove  a  proposition  it  is  necessary  to  find  some 
^admitted  fact  or  truth  which  is  inconsistent  with  it. 
Tor  instance,  if  we  can  show  that  the  contrary  or  con- 
tradictory of  a  proposition  is  true,  the  proposition 
must  be  false.  More  concretely,  if  we  have  an  A  propo- 
sition, the  contradictory  would  be  an  O  proposition ;  if 
we  can  show  that  O  is  true,  A  is  necessarily  false,  and 
to  show  the  truth  of  O  we  need  find  only  one  real  ex' 

166 


INDIRECT   PROOF  167 

ception  to  A.  Showing  the  truth  of  E  would  also  dis- 
prove A;  but  E  is  a  universal  proposition,  and  it  is 
obviously  much  more  difficult,  in  ordinary  circum- 
stances, to  prove  a  universal  than  it  is  to  prove  a  par- 
ticular. Similarly  the  truth  of  I  or  of  A  would  mean 
the  falsity  of  E,  etc. 

In  indirect  proof,  we  disprove  the  contradictory,  not 
the  contrary,  for  the"  falsity  of  the  contrary  does  not 
prove  the  truth  of  the  proposition,  since  both  contraries 
may  be  false ;  but  if  the  contradictory  is  false,  the  prop- 
osition must  be  true,  for  one  of  two  contradictories 
must  be  true.  Suppose  then  that  we  wish  to  prove 
an  A  proposition :  if  we  can  show,  in  any  way,  that  the 
corresponding  O  proposition  would  be  false  or  absurd 
— contrary  to  fact  or  reason — our  thesis  is  proved. 

The  contradictory  is  usually  disproved  by  show- 
ing that  some  of  its  necessary  consequences  are  ab- 
surd. 

Indirect  proof  is  frequently  employed  in  geometry 
and  it  is  there  that  the  best  examples  of  it  are  to  be 
found.  It  is  also  a  frequent  resource  in  political  de- 
bate, but  in  that  field  the  facts  are  so  complicated  and 
the  matter  of  establishing  any  proposition  so  liable  to 
error  chat  the  grounds  of  any  conclusion  established 
in  this  way  must  be  very  carefully  examined. 

We  shall  consider  briefly  two  other  special  forms  of 
proof,  which  are  perhaps  reducible  to  direct  proof,  but 
they  are  apparently  very  different  from  what  we  find 
in  the  syllogism  and  they  will  therefore  be  considered 
separately.  The  first  is  found  in  geometrical  reasoning. 

PROOF  IN  GEOMETRY. — In  geometrical  proof  we  seem 


168  PROOF    AND    DISPROOF 

to  be  founding  a  universal  conclusion  upon  a  single 
case ;  how  is  it  possible  for  us  to  have  perfect  confidence 
in  a  conclusion  which  seems  at  first  sight  to  be  an  in- 
duction from  one  isolated  figure?  If  the  individual 
peculiarities  of  the  figure  had  anything  to  do  with  sup- 
porting the  conclusion  the  latter  would  of  course  be 
of  very  slight  value ;  we  should  have  no  assurance  that 
the  next  example  might  not  be  inconsistent  with  the 
conclusion.  The  certainty  of  the  conclusion  rests  upon 
the  fact  that  the  figure  used  in  the  demonstration  is,  in 
all  essential  respects,  like  every  other  figure  to  which 
the  proof  is  supposed  to  apply.  The  figure  employed 
is  purely  symbolical ;  it  stands  for  certain  universal  re- 
lations. If  the  truth  of  the  conclusion  follows  from 
the  characteristics  which  the  present  figure  has  in  com- 
mon with  all  others  of  the  class,  then  it  will  be  true  for 
all  such  figures,  and  the  peculiar  characteristics  will 
have  nothing  to  do  with  the  case.  The  major  premise 
underlying  demonstration  by  means  of  figures  is  this: 
"  The  present  figure  is  an  adequate  representative  of 
all  figures  to  which  the  present  proof  applies." 

The  second  special  form  of  proof  which  we  shall 
examine  is  found  in  what  is  known  as  mathematical  in- 
duction. 

PROOF  BY  MATHEMATICAL  INDUCTION. — The  follow- 
ing illustration  is  a  typical  example  of  reasoning  of  the 
sort  just  mentioned.  "  If  we  take  the  first  two  consecu- 
tive odd  numbers,  1  and  3,  and  add  them  together  the 
sum  is  4,  or  exactly  twice  two;  if  we  take  three  such 
numbers,  1  +  3  +  5,  the  sum  is  9,  or  exactly  three  times 
three;  if  we  take  four,  namely  1  +  3  +  5  +  7,  the  sum  is 


MATHEMATICAL    INDUCTION          169 

16,  or  exactly  four  times  jour;  or  generally,  if  we  take 
any  number  of  the  series,  l  +  3  +  5'  +  7  +  ....,  the  sum 
is  equal  to  the  number  of  terms  multiplied  by  itself. 
Any  one  who  knows  a  little  algebra  can  prove  that  this 
remarkable  law  is  universally  true,  as  follows  :  Let  n  be 
the  number  of  terms,  and  assume  for  the  moment  that 
this  law  is  true  up  to  n  terms,  thus: 


1+3+5+7+  ____  +(2n-I)=n2 

Now  add  2ft  +  1  to  each  side  of  the  equation.     It  fol- 
lows that: 


1+3+5+T+  ____ 


But  the  last  quantity,  7&2  +  2n  +  l,  is  just  equal  to 
(n  +  1)2  ;  so  that  if  the  law  is  true  for  n  terms  it  is  true 
also  for  n  +  1  terms.  We  are  enabled  to  argue  from 
each  single  case  of  the  law  to  the  next  case  ;  but  we 
have  already  shown  that  it  is  true  of  the  first  few  cases, 
therefore  it  must  be  true  of  all."  L  If  what  is  true  of 
any  case  is  true  of  the  one  following  it,  it  will  be  true  of 
all  cases  whatsoever.  It  sometimes  happens  that  some- 
thing is  true  of  a  great  many  successive  cases  without 
being  really  general.  To  quote  again  from  Jevons: 
"  It  was  at  one  time  believed  that  if  any  integral  num- 
ber were  multiplied  by  itself,  added  to  itself,  and  then 
added  to  41,  the  result  would  be  a  prime  number,  that 
is,  a  number  which  could  not  be  divided  by  any  other 
integral  number  except  unity  ;  in  symbols,  x2  +  x  +  41 
=  prime  number.  This  was  believed  solely  on  the 
ground  of  trial  and  experience,  and  it  certainly  holds 
l  Jevons,  Lessons  in  Logic,  pp.  220-221. 


170  PROOF    AND    DISPROOF 

for  a  great  many  values  of  x .  .  .  .  No  reason,  how- 
ever, could  be  given  why  it  should  always  be  true.  .  .  . 
it  fails  when  x  =  40."'  "  We  can  perceive  no  simi- 
larity between  all  prime  numbers  which  assures  that  be- 
cause one  is  represented  by  a  certain  formula,  also 
another  is ;  but  we  do  find  such  similarity  between  the 
sums  of  odd  numbers." 

Here,  as  elsewhere,  if  one  or  a  few  cases  are  adequate 
representatives  of  a  whole  class  of  cases,  what  is  true 
of  the  present  case  or  cases  will  be  true  of  all,  and  a 
universal  conclusion  can  be  drawn  from  a  single  -case. 
The  great  difficulty  in  ordinary  inductions  is  to  be  sure 
that  the  given  case  is  an  adequate  representative.  Or- 
dinarily the  facts  are  very  complex  and  the  inspection 
of  a  single  case  is  not  sufficient  to  show  us  the  charac- 
teristics which  an  adequate  representative  of  the  class 
should  possess.  In  other  words,  we  do  not  know  what 
circumstances  are  relevant.  In  selecting  cases  for  the 
application  of  the  several  inductive  methods,  the  selec- 
tion is  for  the  purpose  of  enabling  us  to  determine  what 
circumstances  are  relevant. 

II.  Failure  to  Prove:  Fallacies. — Let  us  examine 
the  various  ways  in  which  proof  may  be  vitiated,  the 
various  fallacies  to  which  reasoning  is  liable.  Some 
of  these  have  been  discussed  already,  but  they  will  be 
mentioned  again  here  and  the  other  fallacies  not  pre- 
viously noted  will  be  examined. 

FALLACIES  OF  LANGUAGE. — In  the  first  place  we  may 
mistake  the  meaning  of  the  premises  owing  to  the  fact 
that  we  have  not  understood  the  language  in  which  they 
are  expressed.  The  Fallacies  of  Amphiboly,  Accent, 
Figure  of  Speech  (see  chapter  v),  are  cases  in  point. 


FALLACIES  171 

Again,  to  mistake  the  general  for  the  specific  use  o£ 
a  term,,  or  the  concrete  for  the  abstract,  or  to  use  a, 
term  in  one  sense  in  one  part  of  the  reasoning  and  ini 
another  sense  in  another  part,  would  render  the  con- 
clusion unsound;  the  Fallacy  of  Accident  must  he- 
guarded  against.  (See  page  55.) 

Once  more,  we  may  mistake  the  collective  for  the  dis-- 
tributive  use  of  a  term  or  vice  versa,  or  we  may  use  a. 
term  in  one  of  these  senses  in  one  part  of  the  reasoning; 
and  in  the  other  sense  .in  another  part ;  this  would  in- 
volve us  in  a  Fallacy  of  Composition  or  of  Division., 
(See  page  57.) 

FALLACIES  OF  ASSUMPTION. — Again,  if  we  use  as  a. 
premise  in  our  reasoning  a  proposition  which  is  not 
established,  such  as  an  insufficiently  verified  inductive 
inference,  our  conclusion  is  not  proved.  It  may  be  true, 
or  it  may  not  be,  but  a  conclusion  is  not  proved  so  long 
as  there  is  a  possibility  that  it  may  be  false.  When  we 
use  a  proposition  of  this  sort  to  support  a  conclusion 
we  are  said  to  commit  the  Fallacy  of  Begging  the  Ques- 
tion, or,  to  use  the  scholastic  term,  Petitio  Principii.  It 
is  frequent  in  cases  in  which  one  has  a  thesis  to  prove 
and  he  sees  that  a  certain  proposition  will  enable  him  to; 
prove  it  (it  may  be  either  premise  in  a  syllogism — or 
both).  He  therefore  assumes  the  truth  of  this  proposi- 
tion on  insufficient  grounds,  sometimes  on  very  slight 
grounds. 

To  decline  to  admit  a  premise  because  we  see  that  it 
necessitates  an  unwelcome  conclusion  is  to  commit  this 
fallacy. 

A  false  categorical  proposition,  an  incorrect  hypo- 
thetical proposition,  or  a  disjunctive  proposition  in 


172  PROOF   AND    DISPROOF 

which  the  disjunction  is  not  complete,  would  also,  if 
used  as  premises,  be  illustrations  of  this  fallacy.  It  is 
not  even  necessary  to  use  a  complete  proposition  to 
commit  this- fallacy ;  the  use  of  a  name  or  an  epithet 
may  lead  to  fallacious  conclusions ;  the  name  or  epithet 
does,  to  be  sure,  imply  a  proposition.  To  argue  that 
this  criminal  should  be  punished,  because  all  criminals 
are  a  menace  to  society,  begs  the  question  if  it  has  not 
been  shown  that  this  man  is  a  criminal.  The  epithet  is 
sometimes  more  dangerous  than  the  implied  proposition 
would  be,  for  we  are  less  likely  to  notice  that  something 
has  been  assumed  when  the  Droposition  is  only  sug- 
gested. 

One  form  of  the  Petitio  Principii  is  Arguing  in  a 
Circle,  or  Circulus  in  Probando.  In  this,  the  premise  is 
simply  the  desired  conclusion  stated  in  other  words.  To 
say  that  man  is  a  conscious  being  because  he  has  mental 
states,  is  to  argue  in  a  circle,  since  to  be  a  conscious 
being  is  to  have  mental  states.  When  the  argument 
is  short  there  is  little  to  be  feared  from  this  fallacy ; 
the  identity  in  meaning  of  the  two  statements  is  easily 
discovered  if  they  come  close  together ;  but  in  a  long 
argument  the  first  may  be  only  vaguely  remembered  by 
the  time  the  second  is  made,  and  if  the  reasoning  has 
not  hitherto  been  questioned  the  fallacy  may  escape 
detection.  A  language  like  English,  which  is  very  rich 
in  synonyms,  offers  very  many  occasions  for  this  fal- 
lacy. 

Another  closely  related  fallacy  is  that  known  as  the 
Fallacy  of  Many  Questions  or  sometimes  Double  Ques- 
tion. One  of  the  traditional  illustrations  is,  "  Have 
you  left  off  beating  your  wife?  "  Whichever  answer  is 


FALLACIES  173 

given,  Yes  or  No,  seems  to  admit  the  truth  of  the  im- 
plication. In  this  fallacy,  the  question  assumes  the 
truth  of  something  which  is  not  proved  or  admitted,  and 
which  may  be  false.  It  demands  a  direct  answer,  and 
no  direct  answer  can  be  given  without  an  apparent  ad- 
mission of  the  thing  assumed. 

FORMAL,  FALLACIES. — There  are  several  fallacies 
which  result  from  the  violation  of  the  principles  of 
syllogistic  reasoning.  These  are  usually  called  the 
Formal  Fallacies,  because  they  are  said  to  result  from 
violating  the  formal  laws  of  the  syllogism,  the  laws  re- 
lating to  the  number  of  terms  and  the  distribution  of 
terms  in  the  syllogism.  We  might  include  also,  Fal- 
lacies of  Illicit  Conversion  and  Obversion.  Creighton 
includes  them  in  Fallacies  of  Interpretation.2  Using 
four  terms  instead  of  three  gives  the  Fallacy  of  Four 
Terms.  Distributing  the  major  term  in  the  conclusion 
when  it  has  not  been  distributed  in  the  premise  gives 
the  Fallacy  of  Illicit  Distribution  of  the  Major  Term, 
and  distributing  the  minor  term  in  the  -conclusion  when 
it  was  not  distributed  in  the  premise  gives  the  cor- 
responding Fallacy  of  the  Minor  Term.  Failing  to 
distribute  the  middle  term  gives  the  Fallacy  of  Undis- 
tributed Middle.  There  are  also  the  Fallacies  of  Two 
Negative  Premises,  and  Two  Particular  Premises. 

This  is  the  way  in  which  violations  of  the  laws  of 
syllogistic  reasoning  have  usually  been  classified.  As 
we  have  already  seen,  these  violations  can  also  be  dealt 
with  as  failures  to  comply  with  the  principles  of  the 
Four  Figures.  The  latter  method  is  less  formal  and 
more  in  accordance  with  our  ordinary  habits  of  thought. 
2  See  his  Logic,  chapter  xii. 


174  PROOF    AND    DISPROOF 

The  Fallacies  of  Hypothetical  Reasoning,  Denying 
the  Antecedent  and  Affirming  the  Consequent,  belong 
in  the  class  just  discussed. 

THE  CONCLUSION  MAY  NOT  FOLLOW  FROM  THE 
PREMISES. — There  is  a  form  of  false  reasoning  known 
as  the  Non  Sequitur.  In  this  the  premises  may  be  clear 
and  true  and  there  may  be  no  fallacies  of  distribution 
or  of  negative  premises,  but  the  conclusion  does  not 
follow  from  the  premises.  It  may  be  true  enough  and 
provable  on  other  grounds  but  it  does  not  belong  to  the 
propositions  on  which  it  has  been  based.  It  was  origi- 
nally called  the  Fallacy  of  False  Consequent  and  had  to 
do  with  hypothetical  reasoning,  but  the  term  Non 
Sequitur  is  now  applied  to  categorical  reasoning  in 
which  the  conclusion  does  not  follow  from  the  premises. 
De  Morgan's  illustration  (quoted  by  Hyslop)  is  as  fol- 
lows: 

Episcopacy  is  of  Scripture  origin. 

The  Church  of  England  is  the  only  Episcopal  Church 
in  England. 

Therefore,  the  church  established  is  the  church  that 
should  be  supported. 

This  fallacy,  like  the  rest,  is  more  likely  to  pass  un- 
noticed in  a  long  argument  than  in  a  short  one. 

A  similar  fallacy,  sometimes  treated  as  a  form  of  the 
last,  is  that  of  False  Cause,  or  Non  Causa  pro  Causa, 
or  Post  Hoc  ergo  Propter  Hoc.  This  consists  in  argu- 
ing that  because  one  thing  has  followed  another,  it  is 
therefore  the  effect  of  that  other,  as  if  one  should  argue 
that  because  a  panic  followed  the  adoption  of  a  certain 
measure,  it  was  therefore  caused  by  that  measure. 

MISSING   THE  POINT. — One   more   fallacy   is   to   be 


FALLACIES 

noted ;  that  in  which  the  argument  is  not  to  the  point. 
The  reasoning  may  with  entire  correctness  prove  some- 
thing but  it  is  not  the  thing  which  was  to  be  proved. 
An  opponent  is  sometimes  charged  with  shifting  the 
ground  of  debate ;  that  means  usually  that  he  is  no 
longer  trying  to  prove  the  thesis  with  which  he  started 
but  something  else  more  or  less  closely  related  to  it. 
This  is  known  as  the  Fallacy  of  Ignoratio  Elenchi. 
Several  forms  have  been  distinguished.  One  of  these  is 
the  Ad  Hominem  argument;  in  this,  instead  of  being 
to  the  point,  the  argument  is  directed  against  the  char- 
acter or  consistency,  etc.,  of  the  opponent  or  some 
other  person.  When  an  advocate  proves  the  prisoner's 
good  character  and  assumes  that  he  has  proved  his  in- 
nocence of  the  crime  with  which  he  is  charged,  he  is 
guilty  of  this  fallacy.  When  a  debater  attacks  his  op- 
ponent instead  of  proving  his  thesis  he  commits  this 
fallacy.  It  is  a  method  of  silencing  an  opponent  but 
not  of  proving  a  case.  Appeals  to  authority,  to  pre- 
judice, to  emotion,  are  all  forms  of  the  fallacy  of 
Ignoratio  Elenchi,  as  is  also  the  argument  in  which  the 
victory  depends  upon  the  fact  that  the  opponent  has 
not  the  information  necessary  to  enable  him  to  meet 
the  argument. 

When  wre  assume  that  a  proposition  is  false  because 
the  arguments  in  its  support  have  been  discredited,  we 
commit  this  fallacy.  The  proposition  is  only  not 
proved,  instead  of  being  disproved.  A  good  cause  may 
suffer  from  bad  arguments  because  of  the  widespread 
tendency  to  commit  this  fallacy. 

In  most  arguments  many  of  the  propositions  involved 
are  unexpressed.  In  such  cases  it  is  often  difficult  to 
know  what  fallacy  to  charge  against  reasoning  which 


176  PROOF    AND    DISPROOF 

is  obviously  unsound.  Suppose  we  have  the  argument, 
"  A  classical  course  is  useless  because  it  trains  for  no 
profession;"  what  fallacies  might  be  charged?  In  the 
first  place  we  might  say  that  the  fallacy  was  a  Non 
Sequitur;  the  conclusion  does  not  follow  from  the 
grounds  which  have  been  stated.  It  might  be  replied 
that  there  was  a  further  premise  understood,  namely, 
"  Every  college  course  which  does  not  train  for  a  pro- 
fession is  useless."  The  fallacy  of  Non  Sequitur  would 
be  disposed  of,  but  it  would  now  be  possible  to  charge 
the  fallacy  of  Begging  the  Question,  in  the  premise 
which  has  been  supplied.  Or  it  might  be  that  the  pre- 
mise understood  was  "  Most  courses  of  study  which  do 
not  train  for  a  profession  are  useless."  That  might 
possibly  be  true,  but  even  admitting  it,  the  reasoning  is 
not  valid,  because  it  violates  the  principles  of  syllogistic 
reasoning. 

In  cases  of  doubt  the  only  way  of  being  certain  that 
we  have  been  fair  to  an  absent  opponent  or  have  met 
all  replies  to  our  criticisms,  is  to  follow  some  such  pro- 
cedure as  that  just  illustrated  and  show  that  if  one 
criticism  can  be  met  another  cannot,  or  that,  if  the  con- 
clusion is  to  be  established,  such  and  such  propositions 
must  be  shown  to  be  true. 

These  fallacies  are  usually  discussed  in  connection 
with  the  syllogism,  but  they  may  occur  in  the  more  com- 
plicated forms  of  reasoning  as  well.  As  we  have 
already  seen,  the  syllogism  is  the  typical  form  of  de- 
ductive reasoning,  but  there  is  much  reasoning  that  is 
extra-syllogistic:  although  this  might  perhaps  be  put 
into  syllogistic  form  such  an  operation  is  unnecessary 
if  the  premises  and  the  steps  in  the  argument  are  clear. 


FALLACIES  177 

In  more  complicated  trains  of  reasoning  which  involve 
induction  as  well  as  deduction  we  must  make  sure  not 
only  of  the  reasoning  processes,  and  of  the  clear  state- 
ment of  the  premises,  but  also  of  the  soundness  of  the 
premises,  and  of  the  grounds  on  which  they  are  based. 

EXERCISES 

In  the  following  exercises,,  supply  missing  premises,  state 
the  Figure  in  which  the  argument  falls,  and  criticise  fully 
the  reasoning,  noting  the  fallacies  of  every  sort: 

1.  Personal   deformity    is    an    affliction    of   nature;    dis- 
grace is  not  an  affliction  of  nature;  personal  deformity  is 
not  a  disgrace. 

2.  All  paper  is  useful,  and  all  that  is  useful  is  a  source 
of  comfort  to  man ;  therefore,  all  paper  is  a  source  of  com- 
fort to  man. 

3.  If  Caesar  were  a  tyrant,  he  deserved  to  die;  but  he 
was  not  a  tyrant,  and  therefore  did  not  deserve  to  die. 

4.  Every  one  desires  his  own  good;  justice  and  temper- 
ance are  everyone's  good;  hence,  every  one  desires  justice 
and  temperance. 

5.  Some  of  the  inhabitants  of  the  earth  are  more  civi- 
lized than  others;  no  savages  are  more  civilized  than  other 
races;  therefore,  no  savages  are  inhabitants  of  the  earth. 

6.  He  must  be  a  Mohammedan,  for  all  Mohammedans 
hold  these  opinions. 

7.  He  must  be  a  Christian,  for  only  Christians  hold  these 
opinions. 

8.  All  valid  syllogisms  have  three  terms;  this  syllogism 
has  three  terms,  and  is  therefore  valid. 

9.  None  but  despots  possess  absolute  power;  the  Czar 
of   Russia   is    a   despot;   therefore,   he   possesses   absolute 
power. 

10.  The  right  should  be  enforced  by  law;  the  exercise  of 
the  suffrage  is  a  right,  and  should  therefore  be  enforced 
by  law. 

11.  Nothing  is  better  than  wisdom;  dry  bread  is  better 
than  nothing;  therefore,  dry  bread  is  better  than  wisdom. 

12.  Every  rule  has  exceptions;  this  is  a  rule  and  there- 


178  PROOF    AND    DISPROOF 

fore  has  exceptions;  therefore,  there  are  some  rules  that 
have  no  exceptions. 

13.  For  those  who  are  bent  on  cultivating  their  minds 
by  diligent  study,  the  incitement  of  academical  honors  is 
unnecessary;  and  it  is  ineffectual  for  the  idle  and  such  as 
are  indifferent  to  mental  improvement;  therefore,  the  in- 
citement   of    academical   honors    is    either    unnecessary    or 
ineffectual. 

14.  Suicide  is  not  always  to  be  condemned,  for  it  is  but 
voluntary   death,   and   this   has   been   gladly   embraced  by 
many  of  the  greatest  heroes  of  antiquity. 

15.  Theft  is  a  crime;  theft  was  encouraged  by  the  laws 
of  Sparta;  therefore,  the  laws  of  Sparta  encouraged  crime. 

16.  Nothing  but  the  express  train  carries  the  mail,  and 
as  the  last  train  was  an  express,  it  must  have  carried  the 
mail. 

17-  Protective  laws  should  be  abolished,  for  they  are  in- 
jurious if  they  produce  scarcity  and  useless  if  they  do  not. 

18.  Whosoever  intentionally  kills  another  should  suffer 
death ;  a  soldier,  therefore  who  kills  his  enemy  should  suf- 
fer death. 

1Q.  The  people  of  the  country  are  suffering  from  famine; 
and  as  A,  B,  and  C  are  people  of  the  country,  they  are 
therefore  suffering  from  famine.3 

20.  Each  of  the  books  in  the  library  is  large;  hence  the 
library  is  large. 

21.  Hunger  is  a  sign  of  health;  therefore,  famine  which 
causes  hunger  is  a  good  thing. 

22.  Arsenic  will  kill  a  man ;  hence,  this  medicine  will  kill 
you  as  it  contains  arsenic. 

23.  The  coat,   hat  and  dress  were  each  in*  good  taste; 
therefore,  the  costume  as  a  whole  was  in  good  taste. 

24.  You  can  always  trust  to  the  majority  to  do  what  is 
right  in  the  long  run;  this  man  is  a  member  of  the  ma- 
jority, and  therefore  he  can  be  trusted  to  do  what  is  right 
in  the  long  run. 

25.  Eating  opium  degrades  and  brutalizes  a  man;  hence 

3  Most  of  the  examples  from  1  to  19  were  borrowed  from  Hys- 
lop's  Elements  of  Logic.  A  good  many  of  them  belong  to  the 
common  stock. 


EXERCISES  179 

DeQuincy   and    Coleridge   were   low    and    degraded    crea- 
tures. 

26.  It  is  wrong  to  take  life  of  fellow  creatures;  hence 
it  is  wrong  to  kill  a  mad  dog. 

27.  Human  life  will  at  some  time  disappear  from  the 
earth,  for  every  man  must  die. 

28.  America  is  a  Christian  country;  hence,  every  Ameri- 
can is  a  Christian. 

29-  The  members  of  the  college  are  students,  teachers, 
and  administrative  officers.  The  members  of  the  football 
team  are  members  of  the  college,  and  hence  are  students, 
teachers,  and  administrative  officers. 

30.  If   it   is   admitted  that  men   who   are   proficient   in 
engraving  are  of  great  service  to  a  community,  it  must  be 
true  that  the  greater  the  degree  of  excellence  possessed  by 
the  counterfeiter,  the  better  for  the  government. 

31.  You   must  allow   that  this   measure  will   do   untold 
good  to  the  country — that  the  whole  community  will  prosper 
and  that  our  nation  will  take  its  place  with  the  foremost. 
You  say  you  grant  all  this  and  still  you  maintain  that  it  will 
ruin  your  particular  section.     Is  not  your  section  a  part  of 
the  nation,  and  will  it  not  be  benefited  as  well  as  the  rest 
of  the  country? 

32.  The  population  of  the  United  States  increased  20% 
between  1890  and  1900;  hence,  the  population  of  Vermont 
must  have  increased  at  that  rate  during  the  same  period. 

33.  Slavery    was    harmful    to    the    development    of    the 
whole  country,  and  hence  to  the  South. 

34.  Policemen   must   arrest   all   persons   who   block   the 
highways  or  interfere  with  traffic.     The  policeman  at  this 
crowded  corner  does  this,  and  should  therefore  be  arrested. 

35.  Kant  held  that  all  the  proofs   for  the  existence  of 
God  were  fallacious.     He  was  therefore  an  atheist. 

36.  At  the  time  of  the  Galveston  flood  men  worked  six- 
teen hours  a  day;  hence,  to  talk  of  an  eight-hour  day  as  a 
necessity  for  the  working  classes  is  absurd. 

37.  The  evidence  of  the  creator  is  the  thing  created. 

38.  Before   you   stands   the   vile   wretch   who   has   been 
accused  of  murder. 

39.  Why  has  man  one  more  rib  than  woman? 


180  PROOF    AND    DISPROOF 

40.  The  candidate  is  very  fond  of  children.,  and  so  no 
doubt  she  would  be  a  good  kindergarten  teacher. 

41.  This  man's  arguments  are  worthless,  for  he  is  no" 
toriously  dishonest. 

42.  In  answer  to  the  argument  that  women,  as  intelli- 
gent human   beings,   are   entitled  to  all  the   privileges   of 
citizenship,   I   ask  you:     Are  not  women  like  our  sainted 
mothers,  who  never  held  a  ballot  in  their  hands,  good  enough 
for  us? 

43.  "  Woman  as  well  as  man  should  have  a  part  in  the 
world's    political   affairs;    for   government   is   nothing   but 
national  housekeeping." 

44.  "  More  coffee  is  consumed  in  the  United  States  than 
anywhere    else,    and    America    has    become    the    strongest 
nation." 

45.  My  opponent   presents   a   formidable   array  of  sta- 
tistics to  prove  that  the  country  is  financially  unfit  for  war; 
to  which  I  am  proud  to  reply  that  the  old  flag  has  never  yet 
touched  the  ground. 

46.  Agassiz    did   not    accept   the    theory    of    Evolution; 
hence  I,  who  know  very  little  of  biology,  am  not  justified 
in  accepting  it. 

47.  This  man  was  a  good  football  player,  and  hence  will 
be  a  good  man  to  write  up  the  present  football  situation. 

48.  A  vacuum  is  impossible,  for  if  there  is  nothing  be- 
tween two  bodies  they  must  be  in  contact. 

49.  The  government  should  be  in  the  hands  of  the  Demo- 
cratic party,  for  the  country  could  not  help  prospering  un- 
der the  supervision  of  the  followers  of  Jefferson. 

50.  It  is  indeed  an  opinion  strangely  prevailing  amongst 
men,  that  houses,  mountains,  rivers,  and  in  a  word  all  sen- 
sible objects,  have   an   existence,  natural  or  real,  distinct 
from   their   being   perceived   by    the   understanding.      But 
with  how  great  an  assurance  and  acquiescence  soever  this 
principle  be  entertained  in  the  world,  yet  whoever  shall  find 
it  in  his  heart  to  call  it  in  question  may,  if  I  mistake  not, 
perceive  it  to  involve  a  manifest  contradiction.     For,  what 
are  the  fore-mentioned  objects  but  the  things  we  perceire 
by  sense?  and  what  do  we  perceive  besides  our  own  ideas 
or  sensations  ?  and  is  it  not  plainly  repugnant  that  any  one 
of  these^  or  any  combination  of  them,  should  exist  unper- 


EXERCISES  181 

ceived? — Berkeley,     Principles     of     Human     Knowledge, 
Sec.  4. 

51.  If   there  were   external   bodies   it   is   impossible   we 
should  ever   come  to  know  it;   and  if  there  were  not  we 
might  have  the  very  same  reasons  to  think  there  were  that 
we  have  now.     Suppose — what  no  one  can  deny  possible — 
an  intelligence  without  the  help  of  external  bodies,  to  be 
affected  with  the  same  train  of  sensation  or  ideas  that  you 
are,  imprinted  in  the  same  order  arrd  with  like  vividness 
in  his  mind.     I  ask  whether  that  intelligence  hath  not  all 
the   reason   to  believe  in  the   existence   of   corporeal   sub- 
stances, represented  by  his  ideas  and  exciting  them  in  his 
mind,  that  you  can  possibly  have  for  believing  the  same 
thing? — Berkeley,     Principles      of     Human     Knowledge, 
Sec.  20. 

52.  In  the  business  of  gravitation  or  mutual  attraction, 
because  it  appears  in  many  instances,  some  are  straightway 
for  pronouncing  it  universal;   and  that  it  attract  and  be 
attracted  by  every  other  body  is  an  essential  quality  inher- 
ent in  all  bodies  whatsoever.     Whereas,  it  is  evident  that 
the  fixed  stars  have  no  such  tendency  towards  each  other; 
and   so  far  is  that  gravitation  from  being  essential  to  bodies 
that  in  some  instances  a  quite  contrary  principle  seems  to 
show  itself;  as  in  the  perpendicular  growth  of  plants  in 
the  elasticity  of  the  air. — Berkeley,  Principles  of  Human 
Knowledge,  Sec.   106. 

53.  "  The   family,  the   state,   religion  and  morality   are 
all  in  danger  in  this  country  on  account  of  divorces,  accord- 
ing to  the  speakers  at  an  Episcopal  meeting  in  New  York 
on  Sunday.     But  are  things  in  so  bad  a  way?  "     In  Eng- 
land, "  so  '  horrible  '  were  the  revelations  of  angry  discon- 
tent with  the  married  state  made  by  hundreds  of  the  cor- 
respondents   of   a   London    paper,   that   it   was    compelled 
recently  to  bring  a  discussion  of  the  marriage  question  to 
an  abrupt  end." 

54.  In     arguing     against     the     Darwinian     Hypothesis, 
Agassiz  is  said  to  have  urged  the  following:     "  If  species 
do  not  exist,  how  can  they  vary  ?  " 

55.  Vegetarianism  is  a  healthy  diet,  for  all  vegetarians 
find  it  so. 

56.  No  educated,  much  less  a  scientific  person,  who  is 


182  PROOF    AND    DISPROOF 

convinced    of    the    immutable    order    of    things,    can   now- 
adays believe  in  miracles. — Buchner,  Force  and  Matter. 

57.  Either   the   laws    of  nature   govern,   or   the   eternal 
reason  governs;  if  both  govern  together  they  must  be  in 
continual    conflict;    the    government    of    the    latter    would 
render  that  of  the  former  unnecessary,  whilst  the  action  of 
unalterable  laws  admits  of  no  personal  interference,  and 
can  on  that  account  scarcely  be  called  governing.     A  main 
point  in  the  proof  that  the  laws  of  nature  are  those  of 
reason  is,  that  by  thought  we  are  able  to  deduce  other  laws 
of  nature  from  those  known  to  us,  so  that  we  find  them  in 
experience,  and  if  this  does  not  happen,  we  naturally  con- 
clude that  we  have  formed  erroneous  conclusions. — Buch- 
ner,  Force  and  Matter. 

58.  In  all  parts  of  knowledge,  rightly  so  termed,  things 
most  general  are  most  strong;  thus  it  must  be,  inasmuch 
as  the  certainty  of  our  persuasion  touching  particulars  de- 
pendeth  altogether  upon  the   credit  of  those   generalities 
out   of  which  they   grow. — Hooker,  Ecclesiastical  Polity, 
i,   12. 

59.  A   spirit   independent   of   nature   cannot   exist;    for 
never  has  an  unprejudiced  mind,  cultivated  by  science,  per- 
ceived its  manifestations.     .     .     .     How  is  it  possible  that 
the  unalterable  order  in  which  things  move  should  ever  be 
disturbed   without  producing   an   irremediable   gap   in   the 
world,  without  delivering  us  and  everything  up  to  an  arbi- 
trary power,  without  reducing  all  science  and  every  earthly 
endeavor  to  a  vain  and  childish  effort? — Buchner,  Force 
and  Matter. 

60.  Order  and  progress  are  two  incompatible  elements. 
Progress   is   accompanied  by   disorder,  by   anarchy.       For 
what  is  progress  if  not  precisely  the  overturning  of  a  given 
social  order  so  as  to  institute  a  new  one? — Draghicesco, 
Le  probleme  de  la  conscience. 

61.  Sunshine  is  necessary  for  plants;  for  vegetable  or- 
ganisms can  not  increase  in  size,  sending  roots  into  the  soil 
and  stems  into  the  air,  without  the  light  and  heat  of  the 
great  solar  luminary. 

62.  Nothing  is  so  bad  that  it  cannot  be  worse. 

63.  "  The  canals  are  not  so  maintained.     They  are  fall- 
ing into  decay  and  disuse.     The  old  boats  are  rotting  and 


EXERCISES  183 

few  new  boats  are  built.  The  business  of  the  canals  falls 
off,  and  the  city  of  New  York,  which  thirty  years  ago  had 
75  per  cent,  of  the  foreign  trade  of  the  country,  now  lias 
less  than  50  per  cent." 

64.  "  Philosophy    bakes    no    bread."      Then  why   waste 
time  upon  it? 

65.  Men  have  a  right  to  vote.     Then  where  is  the  justice 
of  depriving  criminals  of  this  right  ? 

66.  Two  and  three  are  even  and  odd;  two  and  three  are 
five;  hence  five  is  even  and  odd. 

67.  To  inflict  capital  punishment  is  to  violate  one  of  the 
commandments  in  the  Decalogue. 

68.  "  The  French  drink  more  wine  than  any  other  nation 
and  in  literature  and  art  they  occupy  a  foremost  place." 

69.  "...  it   deals    with   the    question    exactly   when   the 
monstrous  tariff  is  to  be  tenderly  revised  by  its   friends. 
The  answer  is  '  Never/     The  thing  cannot  be  done  in  pros- 
perous  times,   because   it   would    disturb   business.       In   a 
period  of  depression,  it  is  out  of  the  question,  as  we  then 
have  troubles  enough  without  opening  Pandora's  box.  When 
affairs  are  just  betwixt  and  between,  neither  very  good  nor 
very  bad,  no  sagacious  Republican  would  think  of  meddling 
with  the  tariff.     Therefore,  we  say  the  exact  position  of  the 
Republicans  is,  that  an  unj  ust  tariff  is  crying  out  for  urgent 
revision,  that  they  are  the  only  ones  who  can  do  the  work, 
and  that  they  will  do  it  just  one  day  after  never." 

70.  "  The  justice  complains  bitterly  that  the  court  has 
been  obliged  to  resort  to  subterfuges  in  order  to  employ 
competent  process-servers,  the  eligible  lists  providing  only 
worn-out  soldiers  who  lack  the  essentials  of  youth,  deter- 
mination, agility  and  vigor.     He  is  therefore  in  favor  of 
going  back  to  the   discredited   system   of  '  pass    examina- 
tions '  or  of  re-enacting  the  starchless  civil  service  law." 

71.  In   the    domain   of   physics,   to   the    exploration   of 
which   Lord   Kelvin  has   devoted   an   honored   lifetime,  he 
would  be  a  bold  man  who  would  cross  swords  with  him. 
But  for  dogmatic  utterance  on  biological  questions  there  is 
no  reason  to  suppose  that  he  is  better  equipped  than  any 
person  of  average  intelligence  ...  in  the  latter   (organic 
nature)  scientific  thought  is  *  compelled  to  accept  the  idea 
of  creative  power.'     That  transcends  the  possibilities  of 


184  PROOF    AND    DISPROOF 

scientific  investigation  .  .  .  Lord  Kelvin,  in  effect,  wipes 
out  by  a  stroke  of  the  pen  the  whole  position  won*  for  us 
by  Darwin.  And  in  so  doing,  it  can  hardly  be  denied  that 
his  present  position  is  inconsistent  with  the  principle  laid 
down  in:  his  British  Association  address  at  Edinburgh  in 
1871. — Extracts  from  letters  written  to  the  London  Times 
apropos  of  Lord  Kelvin's  assertion  regarding  the  limits  of 
science.  (Reprinted  in  Science.) 

72.  The    fact    is    so    improbable    that    extremely    good 
evidence  is  needed  to  make  us  believe  it;  and  this  evidence 
is  not  good,  for  how  can  you  trust  people  who  believe  in 
such  absurdities? 

73.  The    axioms    of   mathematics    and   the    fundamental 
moral  principles  are  inborn ;  for  they  are  accepted  by  every- 
body.    Moreover  no  reasonable  being  can  deny  them  when 
he  understands  what  they  mean. 

74.  I    may    doubt    everything    except    that    I    think.      I 
think,  therefore  I  exist. 

75.  A  parliamentary  government  is  sure  to  fail  in  the 
long  run ;  a  battle  may  be  won  by  a  poor  general  but  never 
by  a  debating  society. 

76.  Can  anything  be  more  ludicrous  than  first  to  build 
all  our  certainty  of  the  assistance  of  the  Holy  Ghost  upon 
the  certainty  of  tradition  and  then  afterwards  to  make  the 
certainty  of  tradition  to  rely  upon  the  assistance  of  the 
Holy  Ghost. — Tillotson,  Rules  of  Faith. 

77.  If  men  are  not  likely  to  be  influenced  in  the  per- 
formance of  a  known  duty  by  taking  an  oath  to  perform 
it,   the   oaths   commonly   administered   are   superfluous;   if 
they  are  likely  to  be  so  influenced,  every  one  should  be 
made  to  take  an  oath  to  behave  rightly  throughout  his  life; 
but  one  or  the  other  of  these  must  be  the  case;  therefore 
either   the   oaths   commonly    administered   are    superfluous 
or  every  man  should  be  made  to  take  an  oath  to  behave 
rightly  throughout  his  life.4  . 

78.  Few   treatises    of   science   convey   important   truths, 
without  any  intermixture  of  error,  irr  a  perspicuous  and  in- 
teresting   form;    and    therefore,    though    a   treatise   would 
deserve  much  attention  which  should  possess  such  excellence, 

*  The  exercises  from  77  to  90  are  from  WhatelyV  Clements  of 
Logic, 


EXERCISES  iss 

it  is  plain  that  few  treatises  of  science  do  deserve  much 
attention. 

79-  No  one  who  lives  with  another  on  terms  of  con- 
fidence is  justified,  on  any  pretense,  in  killing  him;  Brutus 
lived  on  terms  of  confidence  with  Caesar;  therefore,  he  was 
not  justified,  on  the  pretense  he  pleaded,  in  killing  him. 

80.  He  that  destroys  a  man  who  usurps  despotic  power 
in  a  free  country  deserves  well  of  his  countrymen;  Brutus 
destroyed   Caesar,  who  usurped  despotic  power  in   Rome; 
therefore,  he  deserved  well  of  the  Romans. 

81.  Nothing  which  is  of  less  frequent  occurrence  than 
the  falsity  of  testimony  can  be  fairly  established  by  testi- 
mony; any  extraordinary  and  unusual  fact  is  a  thing  of 
less  frequent  occurrence  than  the  falsity  of  testimony  (that 
being  very  common)  ;  therefore,  no  extraordinary  and  un- 
usual fact  can  be  fairly  established  by  testimony. 

82.  Testimony  is  a  kind  of  evidence  which  is  very  likely 
to  be  false;  the  evidence  on  which  most  men  believe  that 
there  are  pyramids  in  Egypt  is  testimony;  therefore,  the 
evidence  on  which  most  men  believe  that  there  are  pyramids 
in  Egypt  is  very  likely  to  be  false. 

83.  He  who  cannot  possibly  act  otherwise  than  he  does, 
has  neither  merit  nor  demerit  in  his  action;  a  liberal  and 
benevolent  man  cannot  possibly  act  otherwise  than  he  does 
in  relieving  the  poor;  therefore,  such  a  man  has  neither 
merit  nor  demerit  in  his  action. 

84.  The  religion  of  the  ancient  Greeks  and  Romans  was 
extravagant   fables    and   groundless   superstitions,   credited 
by  the  vulgar  and  weak,  and  maintained  by  the  more  en- 
lightened,  from   selfish   or   political  views ;   the   same  was 
clearly  the  case  with  the  religion   of  the  Egyptians;  the 
same  may  be  said  of  the  Brahminical  worship  o£  India,  and 
the  religion  of  Fo,  professed  by  the  Chinese;  the  same,  of 
the  mythological  systems  of  the  Peruvians,  of  the  stern  and 
bloody  rites  of  the  Mexicans,  and  those  of  the  Britons  and 
Saxons ;  hence  we  may  conclude  that  all  systems  of  religion, 
however   varied    in   circumstances,    agree   in   being   super- 
stitions   kept    up    among    the    vulgar,    from    interested   or 
political  views  of  the  more  enlightened  classes. 

85.  What  happens   every  day  is  not  improbable;   some 
things  against  which  the  chances  are  many  thousands  to 


186  PROOF    AND    DISPROOF 

one,  happen  every  day;  therefore,  some  things  against 
which  the  chances  are  many  thousands  to  one  are  not  im- 
probable. 

86.  The  principles  of  justice  are  variable;  the  appoint- 
ments of  nature  are  invariable;  therefore,  the  principles  of 
justice  are  not  appointments  of  nature. 

87.  Of  two  evils,  the  less  is  to  be  preferred;  occasional 
turbulence,  therefore,  being  a  less  evil  than  rigid  despotism, 
is  to  be  preferred  to  it. 

88.  No  evil  should  be  allowed  that  good  may  come  of  it; 
all  punishment  is  arr  evil;  therefore,  no  punishment  should 
be  allowed  that  good  may  come  of  it. 

89.  Repentance  is  a  good  thing;  wicked  men  abound  in 
repentance;  therefore,  wicked  men  abound  in  what  is  good. 

90.  If   the    exhibition    of    criminals,    publicly   executed, 
tends  to  heighten  in  others  the  dread  of  undergoing  the 
same  fate,  it  may  be  expected  that  those  soldiers  who  have 
seen  the  most  service,  should  have  the  most  dread  of  death 
in  battle;  but  the  reverse  of  this  is  the  case;  therefore,  the 
former  is  not  to  be  believed. 

91.  Why  does  a  ball,  when  dropped  from  the  masthead 
of  a  ship  in  full  sail,  fall  not  exactly  at  the  foot  of  the 
mast  but  nearer  the  stern  of  the  vessel? — Davis,  Logic. 

92.  "  The  impious,  whoever  he  may  be,  ought  not  to  go 
unpunished.     For  do  not  men  regard  Zeus  as  the  best  and 
most  righteous  of  the  gods?     And  even  they  admit  that  he 
bourrd  his  father  because  he  wickedly  devoured  his  sons." — 
Plato,  Euthyphro. 

93.  The    soul    is    unchangeable;    the    unchangeable    is 
simple;  the  simple  is  indissoluble;  the  indissoluble   is  in- 
destructible; therefore,  the  soul  is  immortal.     See  Plato, 
Phaedo. 


PART  II 
SUPPLEMENTARY    METHODS 


CHAPTER  I. 
STATISTICS 

The  value  of  any  cnnrlufiinn  drpmrh  Inrgply 
the  soundness  of  the  premises  from  which  it  is  drawn; 
a  great  many  of  these  premises,  as  we  have  seen,  are 
inductions  from  particular  facts.  When  these  inductive 
inferences  have  been  tested  by  one  or  another  of  the 
"  Inductive  Methods  "  they  can  be  regarded  as  trust- 
worthy ;  but  the  successful  application  of  the  methods 
presupposes  a  fairly  complete  analysis  of  the  phe- 
nomena under  investigation,  for  it  is  by  this  analysis 
that  we  determine  the  circumstances  in  which  the 
phenomenon  occurs.  If  we  cannot  determine  the  cir- 
cumstances it  is  obvious  that  we  cannot  apply  the 
Methods.  It  might  seem  to  follow  from  this  that  if 
the  circumstances  in  which  a  phenomenon  occurs  are  so 
complex  as  to  defy  analysis,  or  if  the  phenomenon  itself 
cannot  be  separated  into  its  elements,  it  would  be  im- 
possible to  make  any  reliable  generalizations  regarding 
the  relations  of  the  phenomenon  in  question.  Or  if  we 
were  quite  unable  to  surmise  which  of  a  multitude  of 
circumstances  was  significant,  or  to  isolate  any  of  them 
by  means  of  the  Methods,  we  could  not  decide  which  was 
causally  related  to  the  phenomenon  and  which  was  not. 
There  are  many  fields  in  which  analysis  is  possible  in 
only  a  slight  degree ;  social  phenomena  and  phenomena 
of  the  weather  are  cases  in  point.  A  moment's  reflec- 

189 


190  STATISTICS 

tion  will  show  the  difficulty  of  applying  the  Method  of 
Agreement,  for  instance,  in  the  study  of  the  weather, 
or  of  the  death  rate.  The  phenomena  are  so  exceed- 
ingly complex  that  anything  approaching  a  complete 
statement  of  their  elements  is  quite  out  of  the  question. 
The  fallibility  of  most  popular  generalizations  in  these 
fields  is  evidence  of  the  difficulty  of  dealing  with  such 
facts.  Must  we  be  content  then  simply  to  guess  at  the 
relations  of  such  phenomena,  with  the  slight  assistance 
which  is  to  be  gained  from  so  precarious  a  method  as 
that  of  Simple  Enumeration?  In  instances  of  this  sort 
another  method,  a  method  which  is  closely  related  to 
the  method  of  Simple  Enumeration,  becomes  important : 
it  is  the  Method  of  Statistics.  In  statistics  we  have  an 
exact  enumeration  of  cases.  If  a  small  number  of  cases 
does  not  enable  us  to  detect  the  causal  relations  of  a 
phenomenon,  it  sometimes  happens  that  a  large  number, 
accurately  counted,  and  taken  from  a  field  widely  ex- 
tended in  time  and  space,  will  lead  to  a  solution  of  the 
problem. 

But  how  can  the  counting  of  cases  aid  in  the  discov- 
ery of  a  causal  relation?  It  does  so  by  showing  the 
relative  frequency  of  the  phenomenon,  its  frequency  as 
compared  with  some  particular  circumstance  or  circum- 
stances. If  we  noted  only  the  phenomenon  itself,  knowl- 
edge of  its  frequency  would  be  of  little  use.  But  if,  in 
a  large  number  of  cases,  taken  from  a  wide  field,  we 
can  find  some  other  phenomenon  correlated  with  the  one 
we  are  investigating,  then  we  have  ground  for  a  con- 
clusion. We  proceed  upon  the  principle  that  if  the  con- 
currence of  two  phenomena  is  merely  a  coincidence,  the 


THE    MEANING    OF    CORRELATION     191 

frequency  of  one  should  make  no  difference  in  the  oc- 
currence of  the  other,  and  conversely  that  if  there  is  a 
correlation,  there  must  be  some  causal  relation.  If  the 
frequency  of  two  phenomena  is  the  same,  or  if  varia- 
tions in  the  frequency  of  one  correspond  to  variations 
in  the  frequency  of  the  other,  or  if  any  change  in  the 
quantity  or  quality  of  one  corresponds  to  changes  in 
the  frequency  of  the  other,  we  are  usually  justified  in 
inferring  that  something  more  than  a  coincidence  is 
present. 

Correlation  may  be  either  positive  or  negative;  in 
positive  correlation  the  presence  of  a  phenomenon  A 
would  mean  the  presence  of  the  phenomenon  B  in  a 
certain  proportion  of  cases  or  in  a  -certain  amount,  and 
so  on ;  in  negative  correlation  the  presence  of  A  would 
of  course  mean  the  absence  of  B  in  a  certain  propor- 
tion of  cases,  and  so  on.  The  relation  between  illiteracy 
and  crime  would  be  an  instance  of  the  former  and  the 
relation  between  vaccination  and  smallpox  would  illus- 
trate the  latter.  The  total  absence  of  correlation  might 
perhaps  be  represented  by  the  relation  between  the 
weather  and  the  day  of  the  month.  Correlation  can  bq 
measured  mathematically ;  that  is  to  say,  it  is  possible 
to  determine  just  what  degree  of  correlation  there  is 
between  two  phenomena.  The  number  which  expresses 
this  is  called  the  coefficient  of  correlation.  Complete 
positive  correlation  would  be  expressed  by  +  100,  com- 
plete negative  correlation  by  -  100,  and  absence  of 
correlation  by  0 ;  A  coefficient  of  +  63  between  two 
phenomena  would  mean  that  one  was  present  in  63  per 
cent,  of  the  cases  in  which  the  other  was  present,  or  that 


192  STATISTICS 

the  amount,  or  amount  of  increase,  and  so  on,  of  one, 
was  63  per  cent,  of  that  of  the  other.1 

Sometimes  2  a  correlation  would  not  prove  a  direct 
causal  relation ;  the  fact  that  the  mortality  among  men 
is  higher  than  that  among  women  and  bears  a  certain 
numerical  relation  to  it,  or  the  fact  that  about  106 
boys  are  born  for  every  100  girls,  are  examples  of  this. 
But  there  is  nothing  peculiar  to  statistics  in  this.  The 
same  thing  appeared  in  connection  with  the  method  of 
Agreement;  here,  as  there,  the  concurrence  of  two  phe- 
nomena may  mean  that  both  are  connected  with  some 
one  underlying  set  of  complex  or  undiscovered  con- 
ditions. And  even  frequent  concurrence  may  be  acci- 
dental, though  a  thoroughgoing  investigation  would 
eliminate  one  which  was  entirely  accidental. 

And  even  if  the  cause  of  a  phenomenon  is  not  dis- 
covered in  this  way,  it  may  be  that  its  frequency 
is  a  matter  of  interest  or  of  practical  importance ;  for 
its  frequency  may  itself  be  a  factor  in  determining  our 
conduct ;  the  number  of  passengers  stopping  at  a  given 
railway  station  or  the  comparative  number  of  boys  and 
girls  in  a  city  may  be  worth  knowing,  even  if  not 
understood.  The  census  reports  contain  a  multitude  of 
facts  of  this  kind ;  eventually  the  causal  relations  of 
many  of  them  may  be  discovered. 

A  statistical  record  like  any  other  enables  us  to  cor- 


1  For    further    discussion,    see    Thorndike,    Mental   and    Social 
Measurements;    Bowley,    Elements    of    Statistics;    Pearson,    The 
Chances  of  Death. 

2  It  will  be  noted  that  the  principles  here  employed  are  related 
to  those  used  in  the  Methods  of  Agreement  and  of  Concomitant 
Variations,  but  here  analysis  may  be  very  incomplete;  frequency 
instead  of  quantity  is  considered,  and  principles  of  the  method 
of  Difference  may  be  employed  in  conjunction  with  the  others. 


STATISTICS  193 

rect  mistakes  of  memory,  and  so  on ;  as,  for  example,  in 
matters  such  as  the  increase  or  decrease  of  crimes,  or 
the  decreasing  or  increasing  coldness  of  winters. 

Usually  the  cause  discovered  by  means  of  statistics 
is  only  a  part  of  the  cause  of  the  phenomenon ;  the  phe- 
nomenon is  the  result  of  a  number  of  circumstances 
working  together  (Composition  of  Causes),  and  not  al- 
ways of  the  same  circumstances  (Plurality  of  Causes). 

We  may  know  already  that  a  certain  circumstance 
is  causally  related  to  a  certain  phenomenon  but  that  it 
is  sometimes  present  without  the  latter  (through  the 
agency  of  a  Counteracting  Cause  or  the  absence  of 
necessary  supplementing  circumstances).  In  such  a 
case  statistics  enable  us  to  discover  how  frequently,  in 
what  proportion  of  instances,  the  phenomenon  will  be 
present  along  with  that  circumstance. 

It  must  be  remembered  that  the  statistical  method 
means  more  than  the  mere  collection  of  cases.  "  With 
the  collection  of  statistical  data,  only  the  first  step  has 
been  taken.  The  statistics  in  that  condition  are  only 
raw  material  showing  nothing.  They  are  not  an  in- 
strument of  investigation  any  more  than  a  kiln  of  bricks 
is  a  monument  of  architecture.  They  need  to  be  ar- 
ranged, classified,  tabulated,  and  brought  into  connec- 
tion with  other  statistics  by  the  statistician.  Then  only 
do  they  become  an  instrument  of  investigation,  just  as 
a  tool  is  nothing  more  than  a  mass  of  wood  or  metal* 
except  in  the  hands  of  a  skilled  workman."  3 

The  processes  used  in  statistical  investigations  differ 
widely,  but  the  following  are  generally  given  in  discus- 
sions of  the  subject:  (1)  The  Collection  of  Material, 
3  Mayo-Smith,  Statistics  .and  Sociology,  p.  18, 


194  STATISTICS 

(2)  its  Tabulation,  (3)  the  Summary,  and  (4)  a  Criti- 
cal Examination  of  its  results.  "  In  collection  and 
tabulation  common  sense  is  the  chief  requisite,  and  ex- 
perience the  chief  teacher ;  no  more  than  a  knowledge 
of  the  simplest  arithmetic  is  necessary  for  the  actual 
processes;  but  since  ...  all  parts  of  an  investi- 
gation are  interdependent,  it  is  expedient  to  understand 
the  whole  before  attempting  to  carry  out  a  part.  For 
summarizing,  it  is  well  to  have  acquaintance  with  the 
various  algebraic  averages,  and  with  enough  geometry 
for  the  interpretation  of  simple  curves,  though  all  the 
operations  can  be  performed  without  the  use  of  alge- 
braic symbols."  4 

The  collection  of  statistics  is  carried  out  by  various 
methods,  some  of  them  very  technical ;  we  can  note  only 
a  few  general  principles  here.  In  the  first  place  the 
data  should  be  collected  over  a  wide  field.  Just  as  in 
the  non-statistical  application  of  the  inductive  methods, 
it  is  necessary  to  collect  data  over  a  field  wide  enough 
to  insure  us  against  mistaking  a  coincidence  for  a  cause 
or  over-emphasizing  the  importance  of  one  out  of  a 
number  of  cooperating  causes,  or  regarding  as  the  sole 
cause  one  which  is  only  one  of  a  number  of  different 
causes  capable  of  bringing  about  the  phenomenon. 

One  danger  to  be  guarded  against  arises  from  the 
failure  of  different  observers  to  use  terms  in  exactly 
the  same  sense.  If  poverty  means  in  some  cases  in- 
ability to  obtain  luxuries  and  in  others,  positive  want, 
we  can  make  little  use  of  statistics  of  poverty. 

Again,  in  many  statistical  investigations,  the  data 
are  obtained  by  means  of  questions  addressed  to  a  great 
*Bowley,  Elements  of  Statistics,  p.  17. 


TABULATION  195 

many  individuals ;  these  questions  should  be  so  worded 
as  to  minimize  as  far  as  possible  the  tendencies  to  care- 
less or  biased  observation,  faulty  memory,  preju- 
dice, dishonesty,  and  imperfect  description  of  the 
facts. 

Tabulation  involves  classification,  and  the  scheme  of 
tabulation  should  be  determined  by  the  purposes  of  the 
investigation — the  problems  which  it  is  intended  to 
solve.  "  In  general,  the  scheme  of  investigation  re- 
quires knowledge  of  certain  groups ;  and  the  totals  re- 
sulting from  tabulation  should  show  the  number  of 
items  in  these,  so  that  after  tabulation,  instead  of  the 
chaotic  mass  of  infinitely  varying  items,  we  have  a 
definite  general  outline  of  the  whole  group  in  question." 

The  totals  and  averages  must  be  so  presented  as  to 
give  a  true  impression  to  an  inquirer.  The  subject  of 
averages  will  be  discussed  more  fully  in  a  later  chapter. 

In  the  summary,  the  aim  is  to  present  the  results  in 
the  clearest,  most  comprehensive,  and  most  suggestive 
way.  The  use  of  averages,  and  representation  by  charts 
and  diagrams,  are  important  here.  In  correlating  the 
results  great  care  is  needed  to  avoid  wrong  interpreta- 
tions. An  increase  in  the  number  of  arrests  might  be 
causally  related  to  increasing  severity  in  the  enforce- 
ment of  law  and  not  to  an  increase  in  crime. 

A  critical  examination  of  the  results  is  possible  only 
when  the  sources  of  the  data,  the  methods  of  their  tab- 
ulation, and  the  mode  of  summarizing  and  drawing 
conclusions,  are  fully  described. 

There  are,  of  course,  many  cases  in  which  the  use  of 
statistics  would  be  unnecessary :  "  In  order  to  prove 
the  relation  between  savagery  and  fetichism  it  is  not 


196  STATISTICS 

necessary  for  us  to  have  statistics  either  of  economic 
condition  or  of  religious  confession.  The  fact  stands 
out  of  itself  simply  by  the  -consensus  of  observation  of 
travelers  and  historians.*"  5 

Where  the  law  of  the  data  is  already  known  the  fre- 
quency of  their  occurrence  is  of  no  further  interest  to 
science.  The  number  of  times  an  acid  has  combined 
with  a  base  to  form  a  salt  is  of  no  importance  to  the 
chemist.  If  we  know  the  laws  and  the  circumstances, 
the  frequency  of  the  event  and  the  times  of  its  occur- 
rence can  easily  be  determined.  "  There  was  some 
interest  in  counting  how  many  eclipses  of  the  moon  and 
sun  took  place  every  year,  so  long  as  they  occurred 
unexpectedly  and  inexplicably ;  since  the  rule  has  been 
found  according  to  which  they  occur  and  can  be  calcu- 
lated for  centuries  past  and  to  come,  that  interest  has 
vanished.  But  we  still  count  how  many  thunderstorms 
and  hailstorms  occur  at  a  given  place  or  within  a  given 
district,  how  many  persons  die,  and  how  many  bushels 
of  fruit  a  given  area  produces,  because  we  are  not  in  a 
position  to  calculate  these  events  from  their  con- 
ditions." 6 

In  other  cases  the  method  of  statistics  may  be  in- 
applicable. "  It  is  difficult  to  express  the  relation  be- 
tween economic  condition  or  religious  feeling  and 
aesthetic  development  in  a  civilized  state,  because  music, 
painting,  and  sculpture  cannot  in  any  way  be  measured 
statistically.  This  is  a  question  of  quality  and  not  in 
any  sense  of  quantity." 

B  Mayo-Smith,  Statistics  and  Sociology,  p.  9. 

6  Sigwart,  Logic,  Part  III,  chap,  iv,  3. 

7  Mayo-Smith,  loc.  cit.     See,  however,  page  210  on  the  ways  of 
applying  exact  methods  in  investigating  such  phenomena. 


DIFFICULTIES  IN  USE  OF  STATISTICS     197 

The  use  of  statistics  is  often  severely  criticised  and 
there  is  much  popular  distrust  of  the  results  attained 
by  their  employment.  There  are,  of  course,  many  dif- 
ficulties to  be  met,  and  many  conclusions  based  upon 
statistics  may  be  false.  They  are  liable  to  most  of  the 
errors  which  occur  in  connection  with  the  handling  of 
individual  facts.  The  original  observations  may  have 
been  faulty ;  in  so  far  as  memory  was  employed,  further 
errors  may  have  entered;  ignorance,  prejudice  or  inac- 
curate statements  may  have  vitiated  whatever  testimony 
was  employed ;  the  records  may  have  been  faulty  or  mis- 
takes may  have  been  made  in  copying;  the  facts  ob- 
served may  not  have  been  representative ;  in  comparing 
different  groups  and  in  noting  correlations  we  may 
mistake  a  mere  coincidence  for  causal  relation.  If  all 
the  precautions  which  are  employed  in  a  scientific  ex- 
amination of  individual  facts  are  made  use  of  here, 
statistics  may  furnish  a  perfectly  valid  basis  for  infer- 
ence. One  practical  difficulty  is  the  unfamiliarity  of 
the  average  reader  with  the  use  of  statistics  and  his 
consequent  inability  to  criticise  them,  and  another  is 
the  frequent  failure  on  the  part  of  the  investigator  to 
furnish  data  for  criticism.8 

s  Interesting  illustrations  of  the  use  of  statistics  are  easy  to 
find.  The  field  of  vital  statistics  is  a  good  one  for  this  purpose. 
One  very  interesting  study  is  Dr.  Allyn  A.  Young's  A  Discussion 
of  Age  'Statistics,  Bulletin  13  of  the  Bureau  of  the  Census. 


CHAPTER  II 

AVERAGES 

The  Arithmetical  Average.  —  In  statisti-cal  investiga- 

tions and  in  all  others  in  which  quantitative  data  are 

employed,  the  use  of  averages  is  often  very  important. 

An  average  is  a  single  quantity  which  represents  two  or 

more  other  quantities.     There  are  several  kinds  of  aver- 

ages ;  that  with  which  we  are  most  familiar  is  the  Arith- 

metical Average.     It  is   obtained  by  adding  together 

the  various  quantities  to  be  averaged  and  dividing  their 

sum  by  the  number  of  quantities.     The  weights  of  the 

members  of  a  college  football  team  were  respectively, 

^  175,  195,  187,  183,  230,  187,  169,  147,  159,  178  and 

\  V  \       185.     The  average  was  181  4-11.     The  average  is  less 

^  ^      cumbersome  than  the  whole  series  of  quantities  or  their 

|  }      sum.     The  greater  the  number  or  size  of  the  quantities 

•W"  the  more  important  does  the  average  become. 

The  average  tells  us  nothing  about  the   individual 


^<- 
\  'Le 


\  Leases.     In  this  example  the  average  is  not  the  same  as 
single  one  of  the  quantities  averaged.    To  take  an- 


other case  :  the  death  rate  of  a  city  gives  no  informa- 
jdptnTregarding  the  death  rate  of  any  given  ward,  nor 
the  number  of  deaths  in  any  given  thousand  of  the 
population.  An  average  simply  serves  as  a  means  for 
representing  the  whole  series  of  quantities  and  for  com- 
paring it  with  other  series.  It  gives  no  information 
regarding  the  homogeneity  of  the  group  :  180  is  the 
average  of  179  and  181  and  also  of  359  and  1. 

There  are  many  cases  in  which  the  simple  form  of  the 

198 


THE    WEIGHTED    AVERAGE  199 

arithmetical  average  or  mean  is  inadequate ;  sometimes 
a  modified  form  of  it  can  be  used. 

The  "Weighted"Average. —  Suppose  we  know  that 
of  six  groups  of  men  the  average  weights  are  respect- 
ively 180,  148,  172,  164,  156  and  152  pounds.  The 
average  is  162.  Can  we  say  that  this  average  satis- 
factorily represents  the  whole  series  of  groups?  That 
will  depend  upon  the  circumstances.  If  the  groups 
were  of  approximately  the  same  size  it  might  be  suffi- 
cient, but  if  in  the  first  group  there  were  10;  in  the 
second,  200 ;  in  the  third,  50 ;  in  the  fourth,  20 ;  in  the 
fifth,  100;  and  in  the  sixth,  150,  our  average  will  be  a 
very  imperfect  representative  of  the  groups.  If,  on 
the  other  hand,  we  multiply  each  of  the  averages  in  the 
series  by  the  number  of  individuals  in  the  group  which 
it  represents  and  divide  the  sum  of  these  products  by 
the  total  number  of  individuals,  we  get  the  average 
154  6-53,  which  is  much  more  accurate  than  that  first 
given. 

180x10+148x900+172x50+164x20+156x100+152x150  =          , 
10     +     200     +     50     +     20     +      100     +      150 

This  is  an  illustration  of  what  is  known  as  a  weighted 
average;  it  is  a  special  form  of  arithmetical  average. 
Where  the  groups  represented  by  a  series  of  averages 
vary  greatly  in  size  we  have  conditions  which  call  for 
"  weighting  the  averages."  "  The  classical  and  most 
useful  application  of  weights  is  the  formation  of  an 
index-number  for  the  change  of  prices  by  fitting  suit- 
able weights  to  the  changes  measured  in  the  prices  of 
various  commodities.  It  is  required  to  find  the  change 
in  the  value  of  gold  when  measured  by  the  prices  of 
other  commodities.  Suppose  that  we  are  given  that 


200  AVERAGES 

prices  of  certain  commodities  between  two  years  were 
in  the  following  ratios : 

Wheat     Silver     Meat     Sugar  Cotton 

First   year    100          100          100          100          100 

Second  year 77  60  90  40  85 

The  simplest  way  to  estimate  for  the  general  fall 
in  price  is  to  take  the  simple  average  of  the  numbers 
in  the  second  year,  viz.,  70.4,  and  say  that  the  general 
prices  in  the  second  year  were  70.4 : 100  1  when  ex- 
pressed in  commodities.  But  it  is  at  once  clear  that 
we  can  not  allow  the  commodities  given  to  have  equal 
influences  on  the  result ;  wheat  is  of  greater  importance 
than  sugar  and  meat  than  silver;  and  again  we  have 
taken  arbitrarily  three  items  to  represent  food  and  one 
for  clothing;  we  need  some  means  of  deciding  relative 
importance.  Suppose  we  decide  that  wheat,  cotton, 
meat  and  sugar  are  respectively  7,  4,  3,  times  and  twice 
as  important  as  silver,  we  should  get  the  following 
table : 

Commodity                Relative  prices  Weight  Product 

in  second  year  Assigned 

Wheat    77                        7  539 

Silver    60                        1  60 

Meat 90                         3  270 

Sugar    40                         2  80 

Cotton    85                         4  340 


352  17  1289 

1289 
Weighted    average    is  — ==75.3 

17 
352 

Unweighted  average  is  — =70.4  2 

5 

1  That  is,  prices  of  commodities  have  fallen  in  this  rate  or  the 
value  of  gold  has  increased  correspondingly. 

2  Bowley,  Elements  of  Statistics,  pp.  111-llC. 


THE    MODE  £01 

It  is  not  always  easy  to  tell  what  weights  should  be 
assigned,  but  considerable  variation  is  possible  without 
much  modification  of  the  result. 

The  Mode. — Another  sort  of  average  which  is  often 
of  great  importance  is  what  is  known  as  the  Mode.  It 
is  that  quantity  which  occurs  with  the  greatest  fre- 
quency. It  is  what  we  frequently  have  in  mind  when 
we  speak  of  the  average  man,  the  average  student,  etc. 
If  in  a  class  of  students,  10  receive  the  grade  A;  20, 
the  grade  B;  50,  the  grade  C;  100,  the  grade  D;  and 
25,  the  grade  F,  the  mode  is  D.  The  mode  very  often 
represents  the  type  more  accurately  than  does  the  aver- 
age. It  gives  us  no  information  about  any  one  indi- 
vidual, but  it  does  indicate  the  sort  of  individual  which 
occurs  more  frequently  than  any  other  sort.  There 
might  well  be  two  or  more  modes  in  a  given  series  of 
quantities.  If  a  class  were  made  up  of  very  bright  and 
very  dull  students,  the  numbers  receiving  the  various 
grades  might  be  A,  25;  B,  50;  C,  20;  D,  100;  and  F, 
25.  The  two  modes  are  at  B  and  D. 

The  mode  is  not  always  easy  to  determine.  In  these 
examples  the  grade  B,  for  instance,  means  a  range  be- 
tween the  grade  which  is  just  high  enough  to  escape 
C  and  that  which  is  the  smallest  fraction  short  of  A. 
It  might  well  be  that  of  the  50  who  were  in  C,  35  were 
in  the  lower  half  of  the  group,  while  of  those  that  were 
in  D  80  were  in  the  upper  half  of  the  group,  so  that  the 
mode  was  really  in  a  group  which  might  be  indicated  by 
the  expression  D  +,  C  — .  The  degree  of  accuracy  re- 
quired in  the  results  would  determine  the  degree  of 
exactness  with  which  we  should  state  the  mode. 

The  mode  is  often  most  useful.  "  The  mode  rather 
than  the  average  in  chest-measurements  is  the  number 


202  AVERAGES 

most  suitable  for  the  ready-made  clothier.  For  pro- 
viding a  post-office  or  a  store,  the  mode  in  postal-orders 
or  prices  of  tea  needs  to  be  known  rather  than  any  other 
average.  Even  the  favorite  coin  in  a  collection  may 
show  the  spirit  of  the  congregation  better  than  the 
arithmetic  average  of  their  contributions."  3 

If  the  series  under  consideration  is  very  irregular  it 
may  be  quite  impossible  to  apply  the  mode. 

The  mode  has  this  advantage  over  the  arithmetical 
average :  it  is  uninfluenced  by  extreme  cases.  In  the 
illustration  on  page  198,  the  average  weight  of  the 
players  would  be  considerably  changed  if  a  player 
weighing  180  pounds  were  substituted  for  the  one 
weighing  230 ;  let  us  see  what  would  happen  in  the  case 
of  the  mode.  More  of  the  quantities  fall  between  180 
and  189  than  within  any  other  equal  range.  This 
range,  180-189,  then,  will  be  the  mode.  The  substitu- 
tion of  the  lighter  player  does  not  modify  the  mode. 
Where  the  number  of  quantities  is  so  small  as  in  this 
illustration,  the  individual  quantities  are  often  men* 
tioned,  but  where  that  is  not  the  case,  the  mode  is  often 
useful  either  as  a  supplement  to  the  arithmetical  aver- 
age or  as  a  subsitute  for  it. 

The  Median. — Another  kind  of  average  useful  in 
many  cases  is  the  Median.  The  Median  is  the  middle 
quantity  in  a  series.  The  weights  of  the  players,  in 
the  order  of  their  magnitude,  were  147,  159,  169,  175, 
178,  183,  185,  187,  187,  195,  230.  The  median  is  183. 
There  are  just  as  many  items  above  it  as  there  are 
below.  The  median,  like  the  mode,  is  unaffected  by  ex- 
treme cases.  "  The  existence  of  any  number  of  million- 
aires has  no  more  effect  on  the  median  income  than  of 
sBowley,  Elements  of  Statistics,  p.  123c 


THE    MEDIAN  203 

an  equal  number  of  other  persons  whose  incomes  are 
above  the  median."  4  The  median  is  very  easy  to  find, 
since  it  is  only  necessary  to  arrange  the  items  in  the 
order  of  their  magnitude  and  find  which  occupies  the 
middle  position.  If  there  is  an  even  number  of  items 
the  median  lies  between  the  two  middle  ones.  Even  if 
our  information  regarding  the  items  is  incomplete  it  is 
often  possible  to  find  the  median  with  a  fair  degree  of 
accuracy.  "  It  may  be  that  in  the  '  wage  census ' 
100,000  persons  whose  wages  were  far  below  the  aver- 
age did  not  come  into  the  returns  at  all,  and  it  is  ver.y 
difficult  to  estimate  their  effect  on  the  arithmetical  aver- 
age, for  want  of  information  as  to  their  earnings ;  but 
to  find  the  median  exactly  we  need  only  know  their  num- 
ber, not  their  earnings  ;  and  if  we  can  assign  a  maximum 
for  their  number,  we  still  can  place  the  median  within 
narrow  limits." 

One  great  advantage  in  the  use  of  the  median  is  to 
be  found  in  the  fact  that  it  can  be  employed  in  dealing 
with  quantities  for  which  no  accurate  measurements 
can  be  obtained.  This  is  especially  important  in  deal- 
ing with  psychological  phenomena.  We  may  be  able 
to  say  that  A  has  a  better  memory  than  B  without  being 
able  to  measure  either,  or  to  state  the  exact  amount 
in  which  A  is  superior  to  B.  The  members  of  a  class  of 
any  size  might  be  arranged  in  the  order  of  their  excel- 
lence in  any  quality  whatever  and  the  median  found  as 
in  the  case  of  numbers.  Francis  Galton,  in  his  Natural 


4  "The  magnitudes  one-quarter  and  three-quarters  up  the  series 
are  called  the  quartels;  those  one,  two,    ....   nine-tenths  of  the 

way  up   are  the   deciles;   those  one,  two,    ninety-nine  hun- 

dredths  up  are  the  percentiles."    Bowley,  Elements  of  Statistics, 
p.  124. 


204  AVERAGES 

Inheritance  and  in  other  works,  developed  and  applied 
this  type  of  average  with  great  effectiveness. 

The  median  may  be  a  very  imperfect  representative 
of  the  type.  If,  in  a  group  of  100  men,  the  weights  of 
50  were  between  190  and  210  pounds,  while  the  others 
ranged  between  130  and  150  pounds,  the  median  would 
be  170.  "  The  median  is  then  chiefly  useful  when  we 
are  dealing  with  a  series  of  objects  of  which  the  main 
part  lie  fairly  close  together ;  a  few  extremes  do  not 
affect  it."  5 

The  Geometrical  Average. — Another  kind  of  average 
useful  in  certain  cases  is  the  Geometrical  average.  It 
is  related  to  the  arithmetical  average  somewhat  as  com- 
pound is  to  simple  interest.  The  population  of  Great 
Britain  and  Ireland  increased  from  12  millions  in  1789 
to  38  millions  in  1890.  Obviously  it  would  be  unsafe 
to  say  that  the  average  increase  was  the  total  increase, 
26  millions,  divided  by  the  number  of  years.  We  should 
expect  the  annual  increase  to  be  greater  as  the  popula- 
tion became  larger,  and,  other  things  being  equal,  the 
two  would  vary  together.  When  we  have  only  two 
quantities  to  deal  with,  the  geometrical  average  is  easily 
found.  In  such  a  case  it  is  the  mean  proportional.  The 
geometrical  average  of  4  and  16  is  8.  The  geometrical 
average  of  5  and  9  is  the  square  root  of  45,  or  '3 
into  the  square  root  of  5.  If  we  were  dealing  with 
three  quantities  the  geometrical  average  would  be  the 
cube  root  of  their  product ;  if  with  five,  it  would  be  the 
fifth  root  of  their  product;  the  general  formula  for  n 
quantities  is  the  nth  root  of  a^  a2.  ...  an.  With  large 
or  numerous  quantities  logarithms  should  be  used.  The 
name  logarithmic  mean  is  sometimes  employed  for  this 
B  Bowley,  Elements  of  Statistics,  p.  126. 


THE    GEOMETRICAL    AVERAGE        205 

kind  of  average.  The  geometrical  or  logarithmic  mean 
is  a  quantity  which  can  be  substituted  for  each  of  the 
quantities  when  they  are  multiplied  together  and  give 
the  same  product,  whereas  the  arithmetical  mean  is  one 
which  can  be  substituted  for  each  of  them  when  they 
are  added  together.  "  Which  mean  we  should  choose  is 
simply  a  question  of  which  we  believe  will  best  represent 
the  facts.  If  the  growth  of  cities  depended  altogether 
upon  the  birth  of  children  within  their  boundaries,  we 
should  naturally  choose  the  geometrical  mean,  for  the 
larger  the  city  (other  things  being  equal)  the  more 
children  will  be  born  in  it.  If,  on  the  other  hand,  the 
population  of  a  city,  like  that  of  a  prison  or  hospital, 
were  made  up  altogether  of  certain  kinds  of  people 
who  were  sent  there  from  without,  there  would  (?)  be 
no  reason  why  a  large  city  should  gain  more  inhabi- 
tants than  a  small  one ;  and  the  more  appropriate  aver- 
age would  be  the  arithmetical.  With  most  cities  the 
natural  rate  of  growth  is  only  partly  geometrical  and 
partly  arithmetical;  so  that  neither  a  series  of  means 
of  the  one  sort  nor  a  series  of  the  other  would  give  a 
wholly  satisfactory  representation  of  the  mean  growth 
from  year  to  year  between  one  census  and  another.  If 
in  any  case  or  set  of  -cases  we  have  reason  to  believe 
that  the  true  mean  lies  somewhere  between  the  arith- 
metical and  the  geometrical,  and  if  we  wish  to  represent 
the  facts  as  accurately  as  they  can  be  represented  bj 
any  mean,  we  must  take  a  mean  that  does  lie  between 
the  two."  6 

Measuring  Deviations  from  an  Average. — It  is  often 
important    when    using    averages    to    know    something 
about  the   closeness  with  which  the  several  quantities 
«  Aikins,  The  Principles  of  Logic,  p.  315. 


206  AVERAGES 

approximate  the  average.  Suppose  for  example,  that 
we  had  a  number  of  different  measurements  of  a  given 
quantity,  say  the  distance  between  two  points:  if  there 
was  little  variation  among  the  measurements  we  should 
usually  regard  their  average  as  a  fairly  accurate  repre- 
sentation of  the  real  quantity ;  but  if  the  variation  were 
very  great  we  might  have  little  or  no  confidence  in  the 
average.  We  shall  need  some  way  of  indicating  the 
amount  of  divergence  within  the  group,  or,  in  other 
words,  the  closeness  with  which  the  several  quantities 
were  grouped  about  the  average. 

1.  One  simple  way  of  doing  this  is  to  take  the  aver- 
age of  the  deviations  from  the  mean  or  average.   Eight 
is  the  average  of  5,  6,  11,  and  10,  and  also  of  1,  2,  15, 
and  14.     The  deviations  in  the  first  series  are  3,  2,  3, 
and  2.    The  average  of  these  deviations  is  1%  or  2/4. 
The  deviations  in  the  second  series  are  7,  6,  7  and  6; 
the  average  deviation  is  6%. 

(The  deviations  are  technically  known  as  "  errors," 
and  their  average  as  the  Average  Error.) 

The  smaller  the  average  error  the  more  closely  are 
the  quantities  grouped  about  the  average ;  and  the  more 
closely  they  are  grouped  about  the  average  the  more 
homogeneous  is  the  group. 

2.  Another  kind  of  average  frequently  employed  in 
this  connection  is  the  Median  or  Probable  Error  (P. 
E.).     Arrange  the  errors  in  the  order  of  their  magni- 
tude ;  the  Median  of  these  will  be  the  so-called  Probable 
Error,  or  the  quantity  within  which  half  of  the  errors 
fall.    Thus,  if  we  have  the  quantities,  1,  3,  6,  8,  9,  12, 
13,  15,  16,  17,  the  average  will  be  10.     The  errors  will 
be  9,  7,  4,  2,  1,  2,  3,  5,  6,  7.     Arranging  these  in  the 
order  of  their  magnitude  we  have  1,  2,  2,  3,  4,  5,  6,  7,  7, 


PROBABLE    ERROR  207 

9.  The  median  will  fall  between  4  and  5,  i.  e.,  4%.  In 
other  words,  4%  is  the  quantity  below  which  half  the 
errors  fall  and  above  which  we  will  find  the  other  half. 
Assuming  that  our  data  are  representative  of  the  class 
of  facts  for  which  they  stand,  any  new  number  standing 
for  things  in  the  same  class  is  as  likely  to  be  within 
4J  of  the  average  as  it  is  to  be  beyond  it.  Exactly  half 
of  the  quantities  already  determined  lie  within  that 
range  (in  the  example,  between  the  numbers  5%  and 
14%),  and  those  already  determined  are,  according  to 
our  supposition,  selected  from  a  wide  enough  field  to  be 
regarded  as  representative  of  the  whole.  An  average 
of  10  with  a  probable  error  of  4.5  means  a  series  of 
quantities  in  which  there  is  a  wide  range  of  variation. 
An  average  of  100  and  a  P.  E.  of  .1  would  indicate 
a  very  homogeneous  group.  In  the  case  of  measure- 
ments it  would  mean  that  there  was  a  close  agreement 
among  the  different  measurements  and  that  the  average 
was  therefore  a  fairly  accurate  approximation  to  the 
true  measurement  (providing,  of  course,  that  constant 
errors  had  been  eliminated). 

"  An  approximation  to  the  probable  error  for  a 
given  series  of  observations  is  obtained  by  arranging  all 
the  observations  in  order  of  magnitude ;  marking  the 
magnitude,  say  a,  above  which  25  per  cent,  of  the  ob- 
servations lie,  and  the  magnitude,  say  &,  below  which 
25  per  cent.  lie.  Half  the  difference  between  a  and  b 
is  the  probable  error.  A  useful  way  of  illustrating  this 
is  to  say  that  if  one  observation  is  chosen  at  random 
out  of  a  group,  it  is  as  likely  as  not  that  it  will  not 
lie  further  from  the  average  than  the  probable 
error."  7 

7  Bowley,  Elements  of  Statistics,  p.  282. 


208  AVERAGES 

Measurement  of  Phenomena. — In  the  more  advanced 
stages  of  most  sciences  the  exact  measurement  of  phe- 
nomena becomes  more  and  more  important.  To  deter- 
mine the  relations  of  a  phenomenon  it  is  not  only 
necessary  to  know  when  it  happens  and  what  its  accom- 
paniments are,  but  also  how  much  of  it  is  correlated 
with  given  amounts  of  other  phenomena.  This  is  evi- 
dent in  the  employment  of  the  methods  of  Concomitant 
Variations,  for  this  method  deals  with  cases  in  which 
the  quantity  of  the  phenomenon  varies.  In  the  method 
of  Residues  also,  quantitative  measurements  are  of  great 
importance;  indeed,  they  are  usually  necessary.  We 
observe  how  much  of  a  given  phenomenon  is  due  to  one 
cause,  how  much  to  a  second,  and  so  on ;  the  remainder 
is  due  to  something  else  not  previously  known  to  be  a 
cause,  etc. 

The  physical  sciences  are  very  largely  quantitative, 
and  more  recently  biology  has  come  to  employ  the 
methods  of  exact  measurements  in  many  of  its  investi- 
gations.8 Measurement  usually  means  the  employment 
of  instruments.  Measurements  of  magnitudes  by  the 
unassisted  eye  are  exceedingly  .inexact,  and  measure- 
ments of  degree  of  quality  are  even  more  so.  White 
marble  painted  in  a  picture  representing  an  architec- 
tural view  by  moonlight  seems  to  be  of  about  the  same 
degree  of  brightness  as  the  actual  moonlit  marble  would 
be,  but  Helmholz  has  calculated  that  it  is  from  ten  to 
twenty  thousand  times  as  bright.9 

To  make  measurements  it  is  necessary  to  fix  units  in 

s  The  name  of  Karl  Pearson  is  most  closely  associated  with 
"  Biometry." 

e  James,  Psychology,  Briefer  Course,  p.  155. 


MEASUREMENT  209 

terms  of  which  the  magnitudes  are  to  be  expressed. 
These  are  usually  determined  arbitrarily.  Units,  stand- 
ards, and  instruments  of  measurement  vary  with  the 
phenomena  to  be  measured  and  can  not  be  discussed 
further  here.10 

Many  errors  may  occur  in  making  measurements,  and 
although  it  is  often  possible  to  eliminate  some  of  them, 
in  the  vast  majority  of  instances  the  measurement  is 
almost  certainly  inexact.  Repeated  measurements  are 
very  seldom  in  exact  agreement.  If  phenomena  were 
broken  up  into  units  of  uniform  magnitude  there  would 
be  less  difficulty,  but  most  phenomena  are  continuous. 
Time  is  not  broken  up  into  minutes,  and  with  the  most 
exact  instruments  it  is  impossible  to  say  when  a  minute 
has  passed.  It  can  be  determined  within  millionths  of 
a  second  but  not  with  absolute  exactness.  For  most 
practical  purposes  rough  measurements  are  sufficient ; 
thus,  for  the  train  dispatcher  it  may  be  enough  to  deter- 
mine the  time  to  a  second,  but  for  astronomical  calcu- 
lations the  smallest  possible  error  may  be  of  serious 
importance.  Most  measurements  are  only  approxi- 
mately true ;  the  problem  is  to  make  the  approximation 
as  close  as  possible. 

There  are  various  conditions  to  be  observed  and 
various  methods  which  can  be  used  in  attempting 
to  get  exact  measurements,  but  they  are  too  technical 
to  be  included  here.11  Constant  errors,  such  as  the 
personal  error,12  can  often  be  determined  and  allowance 
can  be  made  for  them.  But  after  all  such  allowances 


10  See  Jevons,  Principles  of  Science,  chap.  xiv. 

11  See  Jevons,  Principles  of  Science,  chap.  xiii. 

12  See  page  23. 


210  AVERAGES 

have  been  made  and  after  all  the  means  for  avoiding 
and  minimizing  error  have  been  employed,  there  yet 
remains  a  margin  of  uncertainty.  In  such  cases  it  is 
possible  to  obtain  a  close  approximation  to  the  true 
measurement  by  taking  a  number  of  measurements  and 
striking  an  average.  After  constant  errors  have  been 
eliminated  any  given  measurement  is  as  likely  to  be  too 
great  as  it  is  to  be  too  small ;  hence,  in  a  large  number 
of  measurements  there  will  probably  be  as  many  of 
those  which  exceed  the  true  magnitude  as  there  are  of 
those  which  fall  short  of  it.  If  the  number  of  measure- 
ments is  small  this  is  more  doubtful,  but  if  a  great  many 
measurements  have  been  made,  we  can  rely  upon  the 
average  with  safety.  The  average  of  all  these  measure- 
ments is  the  closest  approximation  which  we  can  get. 
Different  kinds  of  average  are  used  ac-cording  to  cir- 
cumstances. The  closeness  with  which  the  several  meas- 
urements are  grouped  about  the  average  will  be 
indicated  here,  as  in  all  cases  of  the  use  of 
average,  by  the  size  of  the  error.  If  the  error  is 
small,  the  measurement  is  reliable,  if  large,  more  doubt- 
ful. 

The  Comparison  of  Quantities  which  Cannot  be 
Measured. — In  the  study  of  many  phenomena  the  prob- 
lem of  quantitative  comparison  is  made  very  difficult  by 
our  inability  to  find  an  exact  quantitative  equivalent 
for  the  phenomena.  "  Many  mental  phenomena  elude 
altogether  direct  measurement  in  terms  of  amount.  How 
many  thefts  equal  in  wickedness  a  murder?  If  the 
piety  of  John  Wesley  is  100,  how  much  is  the  piety  of 
St.  Augustine?  How  much  more  ability  as  a  dramatist 
had  Shakespeare  than  Middleton?  What  per  cent,  must 


COMPARISON    OF    QUANTITIES 

be  added  to  the  political  ability  of  the  Jewish  race  to 
make  it  equal  to  the  Irish  race?  .  .  .  Nevertheless, 
such  phenomena  can  be  measured  and  subjected  to  quan- 
titative treatment."  13 

The  method  to  be  employed  in  such  cases,  as  Pro- 
fessor Thorndike  goes  on  to  show,  is  to  arrange  the 
individuals  (or  other  unmeasurable  data)  according  to. 
their  rank.  We  may  not  be  able  to  say  how  much 
more  eminent  A  is  than  B,  but  if  we  can  say  that  A  is 
in  the  first  rank,  whereas  B  is  in  the  tenth,  we  have  a 
true  basis  of  comparison.  We  cannot  measure  directly 
the  intelligence  of  students  in  a  class,  but  we  may  be 
able  to  say  that  one  is  in  the  first  group,  whereas  an- 
other is  in  the  fourth.  Thus,  with  any  number,  it  would 
be  possible  to  give  each  his  proper  place  in  the  group. 
This  method  can  be  applied  to  any  trait  whatever.  The 
great  difficulty  is  in  making  sure  that  the  ranking  is 
correct.  Single  observations  and  individual  judgments 
are  subject  to  the  same  errors  here  as  in  all  other  cases 
of  observation. 

EXERCISES. 

1.  What  sort  of  average  should  be  employed  in  deter- 
mining the  standard  size  of  an  article  to  be  manufactured 
in  large  quantities — say  window  shades  ? 

2.  What  sort  of  average  should  be  employed  in  getting 
a  number  to  represent  the  value  of  articles  in  a  large  and 
varied  invoice  of  merchandise? 

3.  If  a  college  had  400  students  in  1880  and  1000  stu- 
dents in  1905,  how  many  did  it  have  in  the  year  which  falls 

is  Thorndike,  An  Introduction  to  the  Theory  of  Mental  and 
Social  Measurements,  p.  18.  This  book  is  an  exposition  of  the 
methods  of  measuring  individuals,  groups,  variability  of  perform- 
ances, etc.,  including  an  exposition  of  the  necessary  modes  of 
presenting  the  facts,  making  calculations,  and  so  oa 


AVERAGES 

half  way  between,  provided  that  the  rate  of  increase  was 
constant  ? 

4.  What  averages  might  be  employed  and  which  would 
be  preferable  in  comparing  the  stature  of  soldiers  in  the 
French  army  with  those  in  the  American  army?     In  com- 
paring the  standing  of  successive  classes  in  college?     In 
comparing  the  salaries  of  members  of  the  faculty  in  two 
universities?     In  comparing  the  rate  of  growth  of  a  large 
university  and  a  small  college? 

5.  How  would  you  indicate  the  degree  of  closeness  with 
which  a  series  of  quantities  approached  their  average? 

6.  What  is  the  difference  between  "  Average  Error  "  and 
"Probable  Error?" 


CHAPTER    III 
PROBABILITY 

THE  conclusions  at  which  we  arrive  by  the  assistance 
of  statistical  methods  and  the  employment  of  averages 
often  fall  far  short  of  the  certainty  attaching  to  scien- 
tific  laws.  The  conditions  required  for  establishing  a 
scientific  law  are  not  fully  present,  and  consequently 
many  of  such  conclusions,  if  not  all  of  them,  lack  com- 
plete verification.  It  does  not  follow,  however,  that 
these  are  valueless.  As  a  matter  of  fact,  most  of  the 
generalizations  which  we  use  in  everyday  life  are  in- 
completely verified;  they  are  extremely  valuable  as  in- 
struments of  knowledge  and  practice;  indeed,  in  the 
absence  of  scientific  laws,  they  are  indispensable.  So 
long  as  their  provisional  character  is  remembered,  there 
is  no  serious  danger  in  using  them. 

A  generalization  of  this  character  is  said  to  be  prob- 
able or  to  possess  some  degree  of  probability.  Proba- 
bility belongs  also  to  particular  propositions.  What  do 
we  mean  by  probability, — by  saying  that  a  statement  is 
probably  true, — that  an  event  will  probably  happen? 
As  we  use  the  term  ordinarily,  it  means  that  we  believe 
we  -have  a  right  to  accept  a»  statement  or  expect  an 
event,  without  feeling  perfectly  certain  of  it.  This 
attitude,  when  it  has  any  justification,  is  based  upon  the 
belief  that  the  grounds  for  accepting  the  statement  are 
stronger  than  those  for  rejecting  it.  It  may  be  that 
we  know  of  no  positive  reasons  against  it,  but  do  not 
regard  the  reasons  in  its  favor  as  conclusive ;  or  it  may 

213 


PROBABILITY 

be  that  there  are  positive  reasons  against  it,  but  that 
those  in  its  favor  are  stronger  or  more  numerous.  These 
reasons  or  grounds  may  be  of  various  kinds.  There  may 
be  many  things  pointing  toward  the  occurrence  of 
such  an  event ;  as,  for  example,  in  the  statement  that 
life  will  probably  at  some  time  cease  upon  the  earth. 
Or  conditions  at  the  present  time  may  be  similar  to 
those  in  which  the  event  has  happened  before ;  the  out- 
come of  an  examination  of  instances  according  to  the 
principles  of  the  method  of  Agreement  gives  a  result 
which  is  usually  only  probable.  In  all  these  cases  it 
is  impossible  not  to  feel  that  a  great  deal  of  vagueness 
attaches  to  our  statement  that  anything  is  probable. 
We  are  not  able  to  say  how  probable  it  is.  There  is 
such  a  thing,  however,  as  mathematical  or  quantitative 
probability.  It  is  based  upon  the  comparative  number 
of  times  an  event  or  connection  of  events  has  occurred. 
If  a  given  circumstance  A  has  been  observed  1000  times, 
and  if,  in  700  cases  of  its  occurrence,  a  phenomenon  B 
has  also  been  present,  we  have  definite  grounds  for  in- 
ferring that  A  will  probably  be  accompanied  by  B 
again.  Every  time  A  and  B  have  occurred  together 
in  the  past  is  an  argument  in  favor  of  their  occurring 
together  in  the  future,  and  every  time  A  has  occurred 
without  B  is  an  argument  against  this  connection;  if 
the  cases  of  the  latter  sort  are  many  in  comparison  with 
those  of  the  former,  we  say  that  the  connection  in  the 
future  is  improbable.  In  the  case  just  mentioned  we 
should  express  the  degree  of  probability  by  the  frac- 
tion %o-  Now  in  dealing  with  the  matter  in  this  quan- 
titative way,  the  term  "  probability  "  has  a  meaning 
which  is  somewhat  different  from  that  in  which  we 


THE    MEANING    OF    PROBABILITY 

ordinarily  use  it.  It  would  mean,  in  the  present  case, 
that  in  the  future  we  should  have  a  right  to  expect  B 
along  with  A  in  seven  cases  out  of  ten.  It  means  noth- 
ing with  regard  to  the  next  case;  we  have  no  more 
reason  for  expecting  one  outcome  than  the  other;  our 
information  has  value  only  for  the  long  run ;  we  have 
no  right  to  expect  that  in  the  next  ten  cases  B  will  be 
present  seven  or  any  other  particular  number  of  times ; 
but  in  the  long  run  we  may  expect  this  proportion  to 
hold  and  the  longer  the  run  the  closer  is  the  approxi- 
mation which  we  may  expect. 

Compare  this  with  one  of  the  former  illustrations, 
"  Life  will  probably  cease  upon  the  earth."  That  does 
not  mean  that  in  a  large  number  of  cases  of  the  sort 
before  us  life  would  cease  in  most  of  them ;  we  are  here 
dealing  with  the  particular  case  and  all  our  arguments 
apply  to  it.  In  quantitative  probability  we  know  noth- 
ing of  the  circumstances  of  the  particular  case ;  it  is 
simply  one  of  a  certain  group,  and  certain  members 
of  this  group  behave  in  one  way,  whereas  others  behave 
in  a  different  way,  and  we  cannot  determine  the  circum- 
stances of  their  behavior  in  either  case.  The  fraction 
expressing  the  degree  of  probability  tells  us  that,  in 
the  past,  the  phenomenon  has  appeared  in  connection 
with  a  certain  circumstance  in  such  and  such  a  pro- 
portion of  cases  and  that  we  may,  unless  there  are 
reasons  to  the  contrary,  expect  this  proportion  to  hold 
in  the  future.  (We  proceed  here  as  elsewhere,  upon 
the  assumption  that  the  future  will  be  like  the  past  and 
that  any  set  of  phenomena  will  behave  in  the  future  as 
it  has  in  the  past,  in  the  absence  of  any  new  and  dis- 
turbing factor.) 


216  PROBABILITY 

Probability,  in  this  connection,  does  not  necessarily 
mean  favorable  odds.  The  event  may  have  occurred  in 
only  one-tenth  of  the  cases ;  its  probability  will  then  be 
%o»  If  it  has  occurred  in  one-half  the  number  of  cases, 
the  probability  will  be  %,  etc. 

The  calculations  of  insurance  companies  are  based 
upon  data  showing  the  number  of  deaths  per  year  for 
individuals  of  various  ages,  and  so  on.  The  great  value 
of  vital  statistics  and  of  statistics  of  many  other  sorts 
is  to  enable  us  to  determine  the  probability  of  events 
which  we  cannot  bring  entirely  under  laws. 

Deducing  the  Probability  of  a  Phenomenon. — There 
are  certain  circumstances  in  which  the  probability  of  a 
phenomenon  may  be  determined  deductively.  For  ex- 
ample, we  can  say  at  once  that  in  tossing  a  coin  the 
probability  of  getting  heads  is  % ;  we  know  that  there 
are  two  possibilities  and  only  two ;  if  the  coin  is  prop- 
erly made  we  know  of  no  reason  why  one  side  should, 
in  any  particular  case  or  in  the  long  run,  fall  any 
oftener  than  the  other.1 

We  say  that  their  chances  are  equal  and  that  the 
probability  of  each  is  %.  In  the  case  of  a  die  the  proba- 
bility that  any  specified  side  will  come  uppermost  is  %. 
There  are  six  possibilities,  all  equal.  In  the  long  run 
we  expect  each  side  to  turn  up  as  frequently  as  any 
other,  viz.,  in  one-sixth  of  the  cases.  The  chances  of 
any  one  are  as  1:5;  one  for,  and  five  against.  If  we 
have  a  bag  containing  twenty  balls,  three  of  which  are 
white  and  the  rest  black,  the  probability  of  drawing  a 
white  ball  is  %o.  In  this  instance  there  are  twenty  pos- 

i  It  is  essential  in  such  calculations  that  there  be  no  known 
factor  favoring  a  given  result  more  than  any  other, 


DEDUCING    PROBABILITY 

sibilities,  three  of  which  would  give  the  desired  result ; 
drawing  a  white  ball  may  be  brought  about  by  realizing 
any  one  of  three  possibilities;  or,  out  of  twenty  possi- 
bilities, three  are  favorable.  In  instances  of  this  sort 
we  have  a  definitely  known  number  of  possibilities,  with 
no  reason  to  believe  that  there  is  anything  tending  to 
bring  about  one  rather  than  another.  The  probability 
of  any  specified  one  among  them  will  be  expressed  by 
a  fraction  having  1  as  its  numerator  and  the  number 
of  possibilities  as  its  denominator.  In  the  case  last 
cited  the  probability  of  drawing  any  particular  ball  is 
Ho-  If  among  these  possibilities  any  number  of  them 
favor  the  realization  of  any  particular  phenomenon,  the 
probability  of  that  phenomenon  will  be  expressed  by 
a  fraction  having  as  its  denominator  the  total  num- 
ber of  possibilities  and  as  its  numerator  the  number  of 
possibilities  favorable  to  the  occurrence  of  the  phe- 
nomenon in  question.  If  all  the  possibilities  were  fa- 
vorable (e.  g.,  if  all  twenty  balls  were  white),  the  frac- 
tion would  be  2%o  or  1,  which  is  the  symbol  for  cer- 
tainty, or  the  upper  limit  of  probability ;  if  none  were 
favorable,  it  would  be  %o  of  0,  the  lower  limit,  or  im- 
possibility. 

Suppose  we  toss  the  coin  twice  (or  toss  two  coins), 
what  is  the  probability  of  getting  heads  both  times? 
There  are  four  possibilities,  as  follows : 

H  H 

H  T 

T  H 

T  T 


218  PROBABILITY 

We  might  get  heads  in  both,  or  heads  in  the  first 
and  tails  in  the  second,  or  tails  in  the  first  and  heads  in 
the  second,  or  tails  in  both.  In  only  one  of  these  does 
heads  come  in  both  throws ;  the  probability  is  therefore 
%.  It  is  the  same  for  two  tails.  For  one  heads  and 
one  tails  it  is  %.  For  heads  in  the  first  throw  and  tails 
in  the  second  it  is  again  %,  and  so  on. 

If  we  should  toss  it  three  times,  the  probability  of 
getting  heads  each  time  would  be  %.  There  are  eight 
possibilities : 

H  H  H  T  H  H 

H  H  T  T  H  T 

H  T  T  T  T  H 

H  T  H  T  T  T 

We  can  get  the  probability  -for  any  number  of  throws 
by  multiplying  together  the  probabilities  for  each  of  the 
several  throws;  for  two  throws,  %  x%,  or  /4 ;  for  three, 

y2  x  y2  x  y2,  Or  ys ;  for  five,  y2  x  y2  x  %  x  %  x  y>,  or  y32, 

and  so  on.  The  results  would  be  the  same  if  we  should 
throw  several  coins  at  once  instead  of  throwing  one 
several  times.  Suppose  we  are  drawing  balls  from  two 
bags ;  one  of  them  contains  three  white  and  seventeen 
black  balls ;  the  other  contains  two  white  and  eight 
black  balls.  What  is  the  probability  of  drawing  a 
white  ball  from  each?  The  probability,  in  one  case,  is 
%o,  and  in  the  other  %o ;  the  probability  of  getting  a 
white  from  each  is  therefore  %oo  or  %oo.  Each  in  one 
bag  might  be  drawn  with  any  one  in  the  other ;  hence 
there  are  200  possibilities,  only  six  of  which  are  favor- 
able ;  each  of  the  two  whites  in  one  bag  might  be  drawn 
with  each  of  the  three  in  the  other. 


DETERMINING    PROBABILITIES 

The  probability  of  getting  any  combination  of  in- 
dependent events  is  thus  obtained  by  taking  the  product 
of  the  probabilities  of  the  several  events. 

If  two  events  are  mutually  exclusive  the  probability 
of  getting  one  or  the  other  would  be  the  sum  of  their 
independent  probabilities.  In  tossing  a  coin,  the  prob- 
ability of  getting  heads  is  %  and  that  of  getting  tails 
is  the  same ;  the  probability  of  getting  one  or  the  other 
is  the  sum  of  the  two  or  1  =  certainty.  In  throwing  a 
die,  the  probability  of  getting  a  five  is  %,  the  proba- 
bility of  getting  a  six  is  the  same,  the  probability  of 
getting  one  or  the  other  is  %. 

In  tossing  a  coin  twice,  "  It  might  be  argued  that 
since  the  probability  of  throwing  heads  at  the  first 
trial  is  %  and  at  the  second  trial  also  %,  the 
probability  of  throwing  it  in  the  first  two  throws 
is  1,  or  certainty.  The  true  result  is  %,  or  the  proba- 
bility of  heads  at  the  first  throw,  added  to  the  exclusive 
probability  that  if  it  does  not  come  at  the  first,  it 
will  come  at  the  second."  2  The  probability  that  it  will 
come  in  the  first  is  %.  The  probability  that  it  will  not 
come  in  the  first  is  also  % ;  the  probability  that  it  will 
come  in  the  second  is  also  %.  The.  product  of  the  two 
last  gives  the  probability  that  if  it  does  not  come  in  the 
first,  it  will  in  the  second.  This  product,  added  to  the 
first  %,  gives  the  probability  that  it  will  come  in  at 
least  one  of  the  two  throws.  There  are,  of  course,  four 
possibilities  in  two  throws,  and  three  of  them  give  at 
least  one  heads. 

If  we  represent  the  probability  that  an  event  will 
happen  by  p,  then  the  probability  that  it  will  not  hap- 

2  Jevons,  Principles  of  Science,  chap,  x,  3. 


220  PROBABILITY 

pen  is  1 — p.     The  probability  in  throwing  a  die  that 
five  will  not  come  up  is  1  -  %  or   %. 

Let  us  suppose  a  case  in  which  six  coins  are  tossed 
(or  in  which  one  coin  is  tossed  six  times)  ;  what  are  the 
probabilities  of  6,  5,  4,  3,  2,  1  and  0  heads  respectively? 
There  will  be  64  possibilities,  as  follows : 

6  0 

HHHHHH  TTTTTT 

5  1 

HHHHHT  HTTTTT 

HHHHTH  THTTTT 

HHHTHH  TTHTTT 

HHTHHH  TTTHTT 

HTHHHH  TTTTHT 

THHHHH  TTTTTH 

4  2 

HHHHTT  HHTTTT 

HHHTTH  THHTTT 

HHTTHH  TTHHTT 

HTTHHH  TTTHHT 

TTHHHH  TTTTHH 

HHHTHT  HTHTTT 

HHTHTH  THTHTT 

HTHTHH  TTHTHT 

THTHHH  TTTHTH 

HHTHHT  HTTHTT 

HTHHTH  THTTHT 

THHTHH  TTHTTH 

HTHHHT  HTTTHT 

THHHTH  THTTTH 

THHHHT  HTTTTH 


PROBABILITY  221 

3  3 

HHHTTT  HHTHTT 

HHTTTH  HTHTTH 

HTTTHH  THTTHH 

TTTHHH  HTHHTT 

HHTTHT  THHTTH 

HTTHTH  THHTHT 

TTHTHH  THTHHT 

HTTHHT  THTHTH 

TTHHTH  HTHTHT 

T  T  H  H  H  T  T  H  H  H  T  T 

One  combination  gives  six  heads,  six  give  five,  etc. 
The  probabilities  for  6,  5,  4,  3,  2,  1,  and  0  heads  are 
respectively  %4,  %4,  15/64,  2%4, 15/64,  %4,  y64.  In  ten 
throws  the  number  of  possibilities  would  be  1024;  the 
numbers  favoring  10,  9,  8,  7,  6,  5,  4,  3,  2,  1,  and  0 
heads  would  be  respectively,  1,  10,  45,  120,  210,  252, 
210,  120,  45,  10,  1.  Examination  will  show  that  these 
series  of  numbers  (1,  6,  15,  20,  etc.,  and  1,  10,  45,  120, 
etc.)  are  the  coefficients  of  the  terms  of  a  binominal 
raised  to  the  power  indicated  by  the  number  of  throws 
(6,  10,  etc.).  In  these  cases  the  phenomena  are  not  mu- 
tually exclusive.  The  fact  that  heads  comes  (or  does 
not  come)  in  any  throw  makes  no  difference  to  the  other 
throws. 

There  are  important  scientific  applications  of  the 
facts  just  brought  out.1  "  Suppose,  for  the  sake  of 
argument,  that  all  persons  were  naturally  of  the  equal 
stature  of  five  feet,  but  enjoyed  during  youth  seven 
independent  chances  of  growing  one  inch  in  addition* 
ijevons,  Principles  of  Science,  chap,  ix,  5. 


PROBABILITY 

Of  these  seven  chances,  one,  two,  three,  or  more,  mny 
happen  favorably  to  any  individual;  .  .  .  out  of  every 
128  people:— 

1  person  would  have  the  stature  of  ,5  feet  0  inches. 
7  persons  "  "      "          "  5    "     1    " 

O1  it  U  U          U  U  K       «          0       « 

35        "        "          "     "         "  5    "     3    " 

35        "        "          "      "         "  5    "     4    " 

4)1  it  «  U  U  U  K        (.1          K        « 

iy  U  4<  U  U  U  ")"()        " 

|  u  a  <c       u  a  5     u       7      " 

The  probability  of  a  stature  of  5  feet  1  inch  would  be 
%28,  the  whole  number  of  possibilities  being  the  de- 
nominator. 

There  are  sometimes  cases  in  which  an  event  has  hap- 
pened  in  all  the  instances  in  which  a  given  circumstance 
or  set  of  circumstances  has  been  present — B  has  always 
followed  A.  What  is  the  probability  of  its  happening 
the  next  time  the  circumstance  or  circumstances  recur? 
Let  the  number  of  times  it  has  happened  be  represented 
by  m.  Then  the  probability  of  its  happening  the  next 
time  is  expressed  by  the  fraction  ^^.  This  may 
be  determined  by  a  series  of  mathematical  operations  or 
more  simply  as  follows :  "  In  this  fraction  the  de- 
nominator represents  the  sum  of  conceivable  cases,  since 
after  m  real  cases  have  occurred  there  are  always  two 
additional  cases,  which  we  can  think  of  as  occurring, 
viz.,  the  repetition  or  non-repetition  of  E  (the  event)  ; 
the  numerator  as  usual  denotes  the  number  of  favorable 
chances.  The  example  usually  adduced  is  that  as  the 


DANGERS    TO    BE    AVOIDED  225 

alteration  of  day  with  night  has  now  been  historically 
attested  for  5,000  years,  the  probability  of  the  same 
alternation  recurring  to-day  =  1,826,214 : 1,826,215  ; 
that  is,  one  may  bet  1,826,214  to  1  on  its  occurring 
again."  3 

Dangers  to  be  Avoided  in  Interpreting  Proba- 
bilities.— Care  is  needed  in  the  employment  and  inter- 
pretation of  probabilities.  When  we  say  that  the  prob- 
ability of  heads  is  %,  we  do  not  mean  that  in  two  throws 
we  shall  get  heads  once,  nor  do  we  mean  that  in  any 
definite  number  of  throws  the  number  of  heads  and  tails 
will  be  equal.  Indeed,  a  run  of  heads  of  any  finite  length 
is  possible.  The  probability  of  a  run  of  ten  is  Vw24. 
But  the  longer  the  series  the  more  closely  should  we 
expect  the  proportion  of  heads  to  approximate  that  in- 
dicated by  the  statement  of  its  probability.  If  heads 
have  come  up  four  times  already  the  probability  of  their 
coming  up  the  next  time  is  still  % ;  the  same  is  true  if 
they  have  come  up  ten  or  any  other  number  of  times. 
The  past  throws  have  nothing  to  do  with  the  present 
or  future.  To  expect  that,  because  a  coin  has  come  up 
heads  several  times  in  succession,  it  is  therefore  more 
likely  to  come  up  tails  the  next  time,4  is  wholly  to  mis- 
understand the  meaning  of  probability.  Indeed,  a  pre- 
ponderance of  heads  in  the  past  throws  would  suggest 
that  the  -coin  was  not  true,  that  there  was  a  hidden 
cause  favoring  heads,  and  that  as  a  matter  of  fact  the 
probability  of  heads  was  greater  than  %.  In  no  case 
does  the  knowledge  of  the  probability  of  an  event  give 
any  definite  information  regarding  the  next  or  any  other 

3  Lotze,  Logic,  Book  IT,  chap.  9. 

4  This  is  sometimes  called  the  "  gambler's  fallacy." 


PROBABILITY 

specified  case.  It  simply  tells  us  that  in  the  long  run 
we  have  a  right  to  expect  a  certain  proportion  of  oc- 
currences, and  the  longer  the  run,  the  closer  the  ap- 
proximation. So  far  as  "  luck,"  pure  and  simple  (fav- 
orable or  unfavorable  accident),  is  -concerned,  we  might 
expect  that,  in  the  long  run,  and  taking  an  infinite  num- 
ber of  individuals,  "  good  luck  "  and  "  bad  luck  "  would 
be  equal,  though  particular  individuals  might  be  always 
lucky  or  unlucky,  or  their  good  or  bad  luck  might  begin 
or  end  at  any  point  whatever.  Bad  luck  in  the  past 
would  be  no  evidence  of  bad  luck  in  the  future.  Of 
course,  a  great  deal  that  we  ordinarily  call  luck  or 
chance  is  really  the  result  of  ability,  foresight,  and  sa 
on,  or  of  their  opposites. 

EXERCISES. 

1.  What  does  each  of  the  following  propositions  mean;1 

(1)  He  is  probably  an  official  of  some  sort. 

(2)  There  is   a  strong  probability  in  favor  of  his 

being  elected. 

(3)  The  probability  of  ten  more  years  of  life  for  a 

man  of  his  age  is  %. 

2.  "  The  probability  that  a  new-born  child  will  live  to 
the  age  of  25  years  is  % ;  and  if  it  lives  to  that  age,  the 
probability  of  its  being  well-educated  is  %;  and  if  it  is 
well-educated,  the  probability  of  its  beirrg  a  distinguished 
person  is  %0*     Calculate  the  probability  of  the  new-born 
child's  being  a  distinguished  pe'rson." — Ray,  Logic. 

S.  Thirty  per  cent,  of  the  men  in  college  are  Freshmen, 
and  twenty  per  cent,  of  the  Freshmen  come  from  the  West. 
What  is  the  probability  that  the  next  student  who  passes 
will  be  a  Freshman  from  the  West?  A  Freshman  and  not 
from  the  West?  Not  a  Freshman? 

4.  What  is  the  probability  that  a  die  will  fall  with  the 
same  side  up  five  times  in  succession  ? 


EXERCISES  225 

5.  What  is  the  probability  that  a  given   side   of  a  die 
will  come  up  at  least  once  in  two  throws  ?     In  three  throws  ? 

6.  In  tossing  a  coin  four  times,  what  is  the  probability 
of  getting  heads  three  times? 

7.  Suppose  that  an  event  had  happened  in  one  thousand 
cases  in  which  a  given  phenomenon  had  been  present  and 
had  never  failed  to  happen  when  the  latter  was  present; 
what  would  be  the  probability  of  its  happening  when  next 
the  phenomenon  was  present? 


SUPPLEMENT  TO  PART  II 


THE  GRAPHIC  METHOD  OF  REPRESENTING 
DATA  AND  THEIR  RELATIONS 

WHEN  large  groups  of  figures  are  to  be  presented 
it  is  often  useful  to  employ  diagrams  which  will  enable 
the  eye  to  grasp  at  once  the  series  as  a  whole.  There 

G.    Britain..  1,633,000 

U.    S 611,500 

France    609,000 

Germany   ....529,000 

Japan    374,000 

Russia    207,500 

Austria    113,000 

are  many  varieties, 
ular    discussions    of 
parative          populations, 
wealth,  navies,  and  so  on, 
often    represent    the    • 
ious    figures    by    lines 
surfaces     which      are 
juxtaposed  as  to  show  at 
once  to  the  ere  the 
Hons  of  the  several  quan- 
tities.      Thus,     the 
nage  of  .the  eight   great- 
est navies  of  the  world  in 
1907    was    approximately  Fig. 


Fig.  1 
op- 

3m- 

>ns, 

on, 

or 

at 

G.B. 

sla- 

U.S. 

an- 

F. 

G. 

J. 

»at- 

R. 

l  in 

A. 

THE    GRAPHIC    METHOD 


227 


as  above.     Or  we  might  employ  rectangles  with  equal 
bases,  or  points  on  a  curve. 

The  relation  between  two  series  of  numbers  or  quan- 
tities may  be  represented  graphically.  Let  us  take  a 
case  in  which  successive  quantities  are  related  to  suc- 
cessive years.  The  population  of  the  United  States 
at  each  census,  from  1820  to  1900,  was  approximately: 
1820,  9  millions;  1830,  12  millions;  1840,  17  millions; 
1850,  23  millions;  I860,  31  millions;  1870,  38  millions; 
1880,  50  millions;  1890,  62  millions;  1900,  76  millions, 
These  facts  could  be  represented  thus : 


Millions  of  population 

*—  *  N3  Co  -C*.  t/i  ON  -vjO( 

ooo  ooo  oc 

(76) 

(62) 

(50) 

(31) 

(23) 

(9) 

(12) 

(17) 

Years  1820   '30 


'40  '50  '60 

FIG.  3. 


'70  '60  '90  1900 


70 


50 


v>  30 
O 
3  20 


Years  1820  '30  '40  '50  '60  '70  '80 

PIG.  4. 


'90  1900 


228       DATA   AND    THEIR    RELATIONS 

In  the  first  figure  the  successive  quantities  are  repre- 
sented by  rectangles  with  equal  bases,  the  years  being 
indicated  on  the  base  line  and  the  population  on  the 


FIG.  5. 


vertical.  Or  we  can  indicate  the  quantities  by  a  series 
of  points  located  according  to  their  size  and  date  and 
join  these  points  by  a  curve,  as  in  figure  4. 


AN    ILLUSTRATION  229 

Figure  5  is  borrowed  from  Bowley's  Elements  of 
Statistics,  and  represents  the  following  data: 


SHILLINGS 


rom  15  to 

16  — 

200 

66 

16 

to 

17  — 

400 

66 

17 

to 

18  — 

100 

« 

18 

to 

19  — 

100 

66 

19 

to 

20  — 

200 

66 

20 

to 

21  — 

200 

66 

21 

to 

22  — 

300 

66 

22 

to 

23  — 

300 

« 

23 

to 

24  — 

500 

66 

24 

to 

25  — 

900 

66 

25 

to 

26  — 

1200 

66 

26 

to 

27  — 

800 

66 

27 

to 

28  — 

700 

66 

28 

to 

29  — 

500 

66 

29 

to 

30  — 

300 

66 

30 

to 

31  — 

300 

66 

31 

to 

32  — 

400 

66 

32 

to 

33  — 

400 

66 

33 

to 

34  — 

500 

66 

34 

to 

35  — 

500 

66 

35 

to 

36  — 

600 

66 

36 

to 

37  — 

400 

66 

37 

to 

38  — 

100 

66 

38 

to 

39  — 

80 

66 

39 

to 

40  — 

20 

Median,  26/9  (26  shillings,  9d)  ;  Quartiles,  24/2, .32. 
Deciles,  20,  23/6,  24/9,  25/8,  26/9,  28/2,  '31,  33/4, 
35/4. 


230       DATA   AND    THEIR    RELATIONS 


Mode,  25/3;  secondary  positions  (modes),  16/6,  36. 

Curves  may  also  be  employed  to  show  the  relations 

between  two  or  more  sets  of  variable  quantities.    Thus: 

Marriage  rate  per  1000 

Imports  and  Exports  per  head 

Price  of  Wheat  per  quarter 


20 

$15 
§10 


m 

i      i   \ 


\     1 


00 


1860 


n  \\ 
< 


•— 


o    tfl 

60 


,1870 


1880 
FIG.  6. 


1890 


There  are  many  opportunities  for  error  in  such  a 
case  as  this.  For  example  if  the  scale  for  the  marriage 
rate  were  twice  as  great,  the  fluctuations  in  the  curve 
'would  appear  to  be  greater  in  comparison  with  those 


THE    PROBABILITY    CURVE             231 

in  the  other  curves.      (See  Bowley,  loc.  cit.)      Great 
caution  is  necessary  in  the  comparison  of  curves. 

n 

\ 

/ 

\ 

/ 

/ 

\ 

\ 

A—  —  ^ 

7 

s 


FIG.  7. 


The  Probability  Curve. — The  curve  represented  by 
Fig.  7  is  of  great  value  in  scientific  investigations.  It 
is  sometimes  known  as  the  Probability  Curve,  or  the 
Normal  Curve  of  Error.  Suppose  a  large  number  of 
measurements  of  a  given  quantity,  or  variations  from 
a  given  standard;  if  no  causes  of  constant  error 
are  present,  errors  of  excess  are  equally  probable  with 
errors  of  the  opposite  sort  as  we  have  already  seen 
(page  210)  ;  moreover  large  errors  are  less  probable 
than  small  errors  and  very  large  errors  are  very  improb- 
able. Let  the  line  Mm  represent  the  correct  measure^ 
ment ;  let  the  part  of  the  curve  to  the  right  of  this  line 
represent  the  positive  errors  (errors  in  excess),  and  the 
part  to  the  left,  those  which  are  negative ;  the  size  of  an 


DATA   AND    THEIR   RELATIONS 

error  would  be  indicated  by  its  distance  from  M  along 
the  base  line.  MF  would  indicate  a  small  positive 
error ;  MS,  a  large  negative  one ;  height  above  the  base 
line  indicates  the  comparative  number  of  the  errors; 
thus  the  line  Ff  means  a  large  number  of  small  errors ; 
the  line  Ss,  a  small  number  of  large  ones.  The  curve 
may  represent  not  only  errors,  but  any  series  of  quan- 
tities grouped  about  a  type,  when  the  causes  of  variation 
are  very  numerous  and  are  independent  of  each  other. 
In  an  earlier  example  it  appeared  that  in  tossing  a  coin 
the  various  possible  series  of  runs  of  heads  or  tails 
could  be  stated  in  a  series  of  figures  which  were  related 
to  each  other  as  are  the  coefficients  in  the  expansion 
of  a  binomial  to  the  power  indicated  by  the  number  of 
throws. 

This  formula  can  be  used  in  any  case  in  which  a 
number  of  independent  variable  factors  is  concerned. 
If  the  number  is  very  large  the  chances  of  the  various 
possible  -combinations  can  be  represented  by  the  curve 
we  are  discussing,  as  for  example,  in  the  case  of  the 
stature  of  adult  males.  Many  factors  enter  into  the 
determination  of  stature,  such  as  heredity,  health  in 
childhood,  kind  and  quality  of  food,  occupation,  and 
so  on ;  the  statures  of  men  in  any  given  community  are 
ranged  on  either  side  of  the  mode  in  such  a  way  as  to 
be  represented  with  substantial  accuracy  by  the  proba- 
bility curve  (or  the  Curve  of  Frequency  or  of  Distri- 
bution, or  the  Normal  Curve  of  Error,  as  it  is  vari- 
ously called). 

Let  us  suppose,  however,  that  some  -constant  factor 
is  introduced  tending  to  alter  stature  in  a  given  direc- 
tion; what  effect  will  this  have  on  the  curve?  It  will 


IRREGULAR    CURVES 


233 


obviously  change  its  form,  for  a  greater  number  of 
cases  will  appear  on  one  side  of  the  former  mode  and  a 
smaller  number  on  the  other;  instead  of  being  sym- 
metrical it  will  be  skewed  to  one  side  or  the  other,  thus : 


FIG.  8. 

The  presence  of  a  skew  always  indicates  the  opera- 
tion of  some  constant  factor.  If  in  tossing  coins  we 
found  such  a  skew  toward  the  side  representing  a  large 
number  of  heads  we  should  have  evidence  of  the  pres- 
ence of  some  constant  factor  favoring  heads. 

Sometimes  the  representation  of  a  series  of  quan- 
tities would  produce  a  curve  of  still  more  irregular 
shape,  such  as  this: 


FIG.  9. 


Such  a  curve  would  show  that  the  group  was  not 
homogeneous ;  that  there  was  really  a  combination  of 
two  groups ;  or  that  certain  factors  were  operative  in 
one  part  of  the  series  and  not  in  another.  Professor 


DATA    AND    THEIR    RELATIONS 

Thorndike1  gives  the  following  curve  as  representative 
of  the  frequency  of  death  at  different  ages,  the  age 


FIG.  10. 

increasing  as  we  go  from  left  to  right.     Certain  factors 
are  operative  in  early  infancy  that  play  no  part  later. 

i  In  his  Theory  of  Mental  and  Social  Measurements,  p.  51.    See 
this  book  for  discussion  of  measurement. 


PART    III 
THE    CONSTRUCTION    OF    SYSTEMS 


CHAPTER  I 
EXPLANATION 

What  is  Explanation  ?-Prob ability,  classification  and 
the  discovery  of  laws  all  have  to  do  with  facts. 
Probability  tells  us  the  frequency  with  which  a  fact 
may  be  expected  to  occur;  classification  puts  the  fact 
into  a  group  of  like  facts,  and  the  better  the  classifica- 
tion from  a  scientific  point  of  view,  the  more  does  the 
placing  of  the  particular  fact  tell  us  with  regard  to 
its  relations  of  resemblance  and  difference  with  other 
facts.  A  law  states  the  conditions  under  which  a  fact 
occurs.  In  which  of  these  cases  can  we  be  said  to 
explain  a  fact? 

The  statement  of  the  frequency  with  which  an  event 
occurs  does  not  explain  the  event.  We  may  say  that 
the  order  of  nature  is  such  that,  unless  some  change  in 
the  conditions  is  introduced,  we  may  expect  an  event  to 
occur  with  the  same  frequency  in  the  future  as  it  has 
manifested  in  the  past;  but  that  is  obviously  very  far 
from  an  adequate  explanation. 

Do  we  explain  an  event  when  we  classify  it?  When 
we  ask  why  a  given  body  fell  to  the  ground,  do  we  ex- 
plain the  phenomenon  by  saying  that  it  was  a  heavy 
body?  Not  entirely,  and  if  we  did  not  already  know 
some  law  holding  for  heavy  bodies,  our  statement  would 
throw  no  light  on  the  subject.  It  is  quite  true  that  a 
statement  of  this  sort  may  be  a  preliminary  to  ex- 
planation. 

237 


238  EXPLANATION 

A  law  tells  us  how  phenomena  of  a  given  sort  be- 
have ;  it  states  the  conditions  of  their  occurrence,  and 
if  we  can  not  say  what  sort  of  thing  a  given  fact  is  we 
can  not  state  its  conditions.  In  bringing  a  fact  under 
a  law  we  first  approach  an  explanation  of  it.  Explana- 
tion has  been  defined  as  (in  positive  science)  "  the 
reduction  of  a  phenomenon  to  the  terms  of  a  general 
principle,  whatever  that  principle  may  be." 

Have  we  reached  a  final  and  -complete  explanation 
of  a  fact  when  we  have  brought  it  under  a  general  prin- 
ciple ?  In  many  cases  this  seems  to  be  sufficient ;  if 
we  are  familiar  with  the  law  and  if  we  can  see  its  bear- 
ing upon  the  fact  in  question,  we  are  ordinarily  content 
with  this  sort  of  explanation.  An  eclipse  of  the  moon 
is  sufficiently  explained  for  ordinary  purposes  if  we 
are  told  that  it  is  caused  by  the  presence  of  an  opaque 
object  between  it  and  the  source  of  its  light.  Or  the 
revolution  of  the  moon  about  the  earth  may  be  ex- 
plained by  saying  that  it  is  the  resultant  of  the  opera- 
tion of  centripetal  and  centrifugal  forces. 

But  there  are  two  further  questions  that  may  be 
asked.  First,  what  are  the  circumstances  in  which  the 
law  operates  in  the  present  case?  and  second,  how  is  the 
law  itself  to  be  accounted  for?  Let  us  consider  the 
second  question:  How  is  a  law  to  be  explained?  The 
answer  is :  By  showing  that  the  law  is  itself  a  case  of 
a  more  general  law.  The  attraction  of  the  earth  for 
bodies  on  its  surface  is  explained  by  showing  that  it 
is  a  case  under  the  law  of  gravitation.  "  It  has  often 
been  found  that  scientific  men  were  in  possession  of 

i  Dictionary  of  Philosophy,  etc.     Ed.  Professor  J.  Mark  Bald- 
win. 


SYSTEMATIZING   DATA  239 

several  well-known  laws  without  perceiving  the  bond 
which  connected  them  together.  Men,  for  instance,  had 
long  known  that  all  heavy  bodies  tended  to  fall  towards 
the  earth,  and  before  the  time  of  Newton  it  was  known 
to  Hooke,  Huyghens  and  others,  that  some  force  prob- 
ably connected  the  earth  with  the  sun  and  moon.  It 
was  Newton,  however,  who  clearly  brought  these  and 
many  other  facts  under  one  general  law,  so  that  each 
fact  or  less  general  law  throws  light  upon  every 
other."  2 

How  far  can  this  be  carried?  Do  we  not  at  last 
arrive  at  laws  which  are  elementary  and  not  to  be  ex-* 
plained  by  reference  to  anything  simpler  or  more  fun- 
damental? Are  we  then  to  regard  these  elementary 
laws  as  inexplicable?  No,  for  reference  to  simpler  and 
more  'fundamental  laws  is  merely  one  method  of  bring- 
ing the  data  into  a  system.  If  the  elementary  law  can 
be  shown  to  be  a  part  of  a  system,  made  up,  for  example 
of  other  elementary  laws,  we  have  all  the  explanation 
which  can  be  demanded.  The  parts  are  explained  by 
being  given  their  proper  place  in  the  whole.  If  the 
whole  were  in  turn  a  part  of  a  larger  whole  it  could  be 
explained  in  the  same  way.  But  suppose  the  whole 
were  ultimate :  could  it  be  explained  ?  Could  the  uni- 
verse,— not  simply  the  physical  universe,  but  the  whole 
of  reality  of  whatever  kind, — could  it  be  explained? 
The  only  kind  of  explanation  which  could  be  given 
would  be  a  statement  of  the  relation  between  this  whole 
and  its  parts,  and  it  is  hard  to  see  what  other  kind 
could  be  asked  for.  One  might  ask  for  the  purpose  of 
it  all,  but  in  the  broad  way  in  which  we  are  conceiving 
.2  Jevons,  Lessons  in  Logic,  p.  268. 


240  EXPLANATION 

of  it,  whatever  purpose  existed  would  be  included  in  the 
whole  itself.3 

The  explanation  of  a  law  (or  fact)  involves  not 
merely  showing  that  it  is  a  case  under  a  general  rule, 
but  also  in  discovering  its  relations  to  other  laws  and 
facts  aside  from  the  general  rule  under  which  it  is 
brought.  Along  with  other  laws  and  facts  it  consti- 
tutes an  interrelated  whole,  and  explanation  might 
better  be  defined  as  giving  the  thing  to  be  explained 
its  place  in  an  organized  system.  We  may  wish  to 
know  not  only  the  general  law  or  laws  under  which  the 
special  case  falls,  but  also  the  other  special  cases  which 
are  related  to  it;  or  in  other  words,  we  may  wish  to 
know  the  general  law  and  also  the  circumstances  of  its 
application  in  the  present  case. 

We  can  distinguish  between  explanation  in  general 
terms  and  specific  explanation.  The  first  consists  in 
assigning  the  general  law;  the  second  in  showing,  in 
addition  to  this,  how  the  general  law  applies.  The 
explanation  of  the  moon's  eclipse  as  given  above  is  of 
the  first  sort ;  if  we  should  supplement  it  by  stating 
that  the  intervening  body  is  the  earth  and  show  how 
the  earth  and  moon  are  situated  with  reference  to  the 
sun,  we  should  have  a  nearer  approach  to  a  specific 
explanation.  If  we  should  go  further  and  give  an  ac- 
count of  the  way  in  which  they  happened  to  be  in  these 
positions  at  this  particular  time  we  should  have  a  still 
more  complete  and  specific  explanation.  The  explana- 
tion of  a  fact,  to  be  absolutely  complete  and  specific, 
would  have  to  contain  a  statement  of  all  the  laws  of 

a  See  Hobhouse,  The  Theory  of  Knowledge,  chapter  on  *'  Ex- 
planation." 


COMPLETE    EXPLANATION 

the  system  to  which  the  fact  belonged  and  also  a  de- 
scription of  all  the  facts  contained  in  the  system.  Or 
otherwise  expressed,  a  complete  specific  explanation 
would  present  all  the  facts  which  were  related  to  the 
one  to  be  explained,  together  with  the  laws  under  which 
each  and  every  one  of  these  relations  fell,  in  a  single 
unified  whole.  If  an  explanation  is  complete  we  can 
start  with  the  laws  and  circumstances  involved  and 
show  that  the  phenomenon  to  be  explained  would  neces- 
sarily follow  from  them.  Such  an  explanation  might 
be  possible  in  some  parts  of  the  field  of  astronomy ;  if 
not  an  absolutely  complete  explanation,  it  could  be  suf- 
ficiently complete  for  all  ordinary  purposes.  Complete 
grasp  of  a  system  would  enable  us  to  reconstruct  the 
past  or  predict  the  future  of  the  system.  The  astrono- 
mer's knowledge  of  the  solar  system  is  so  thorough  that, 
starting  from  the  present  position  of  any  member  of 
the  solar  system  and  knowing  the  relation  in  which  it 
stands  to  each  of  the  others,  he  is  able  to  calculate  the 
present  position  of  any  of  the  others  and  also  to  recon- 
struct their  relative  positions  in  the  past  or  to  predict 
their  positions  in  the  future ;  he  can  state  the  number 
and  dates  of  eclipses  which  took  place  a  thousand  years 
ago  and  he  can  calculate  the  relations  of  any  member  of 
the  system  to  any  other  at  any  given  time.  The  only 
limits  to  such  calculations  are  those  which  result  from 
an  imperfect  knowledge  of  the  solar  system  itself  and 
ignorance  of  many  possible  disturbances  from  without. 
If  a  system  were  entirely  isolated  and  if  its  laws  were 
completely  known,  then  a  description  of  the  system  at 
any  given  time  would  make  possible  a  description  of  it 
at  any  other  time.  Needless  to  say  there  is  no  system 


EXPLANATION 

of  facts  in  nature  which  is  entirely  independent  of  the 
rest.  Every  system  of  facts  is  related  to  every  other 
system,  either  directly  or  indirectly.  To  get  a  com- 
plete explanation  of  any  single  fact  it  would  be  neces- 
sary to  know  the  whole  system  of  nature.  To  a  knowl- 
edge of  all  the  laws  of  nature  and  all  their  relations 
to  each  other,  it  would  be  necessary  to  add  a  complete 
description  of  the  relations  of  the  parts  of  the  system 
to  each  other.  Then  we  could  have  an  explanation  of 
the  fact  which  would  show  its  relations  to  the  whole 
and  to  every  part  of  the  whole.  Obviously,  an  ex- 
planation of  this  sort  can  not  be  given  for  any  fact. 
If  it  could  be  given  for  one  it  could  be  given  for  all. 
In  this  sense,  Tennyson's  lines  are  literally  true: 

"  Flower  in  the  crannied  wall, 

If  I  could  understand 
What  you  are,  root  and  all,  and  all  in  all, 
I  should  know  what  God  and  man  is." 

Sometimes  we  are  satisfied  with  an  explanation  in 
general  terms,  in  terms  of  some  familiar  law.  Some- 
times we  call  for  an  explanation  of  the  law  and  are 
satisfied  if  it  can  be  referred  to  some  more  general  law 
or  to  some  familiar  system.4 

4  Each  of  the  "  explanatory "  sciences  deals  with  some  limited 
group  of  facts  and  attempts  to  discover  the  system  of  laws  which 
holds  within  that  field.  Every  one  of  the  positive  sciences  takes 
for  granted  certain  general  principles,  valid  for  all  knowledge,  and 
tries  to  discover  a  system  of  laws  which  shall  be  valid  for  its  own 
field.  A  demand  for  the  explanation  of  a  physical  fact,  which  is 
not  satisfied  with  a  statement  of  its  relation  to  other  physical 
facts  in  terms  of  physical  laws,  is  not  a  problem  for  the  science 
of  physics.  Ultimate  explanations  are  for  an  ultimate  science; 
philosophy  is  sometimes  defined  as  this  ultimate  science.  The 
laws  which  underly  all  the  other  sciences  would  be  the  province 


THE    AIM    OF    MOST    SCIENCES 

The  aim  of  most  of  the  sciences  is  not  to  explain  par- 
ticular facts  but  to  furnish  the  general  laws,  which  may 
be  employed  in  explanation  of  facts  in  a  given  field.  A 
Science  like  mechanics,  for  example,  "  lays  down  prop^ 
ositions  which  are  true  in  the  same  way  of  all  fluids,  all 
gases,  etc.,  and  represents  them  as  general  consequences 
of  general  presuppositions."  "  It  does  not  descend 
into  the  whole  manifold  of  the  given,  inasmuch  as  it 
deals  only  with  events  which  take  place  in  a  similar 
manner  in  bodies  differing  in  many  other  respects. 
That  this  or  that  phenomenon  falls  under  these  laws  is 
a  matter  for  subsumption  in  dealing  with  the  particu- 
lar ;  it  is  not  necessary  to  the  completeness  of  the  ar- 
rangement as  a  whole.  The  mechanical  theory  of  gases 
disregards  their  chemical  differences  in  so  far  as  they 
do  not  affect  its  special  province  by  giving  rise  to  dif- 
ferences of  specific  gravity ;  it  is  no  part  of  its  task  to 
enumerate  how  many  sorts  of  gases  there  are:  it  is 
enough  to  say  that  if  a  body  is  a  gas  it  conforms  to 
certain  laws  of  compressibility,  of  expansion  by  heat, 
or  of  capacity  for  heat,  etc." 

Corresponding  statements  might  be  made  about  any 
one  of  the  sciences  which  aim  at  the  discovery  of  laws 
(as  distinguished  from  the  classificatory  sciences,  which 
aim  only  at  the  complete  classification  of  facts). 

of  such  a  universal  science.  It  would  be  related  to  the  particular 
sciences  as  they  are  related  to  the  concrete  data  which  they  in- 
vestigate. It  would  not  be  complete  till  each  of  them  was  com- 
plete, nor  could  any  of  them  be  final  until  it  had  reached  its 
goal;  just  as,  in  any  one  of  them,  no  fact  is  completely  known 
unless  the  general  body  of  laws  is  known,  and  the  body  of  laws 
can  not  be  completely  known  until  every  fact  can  be  accounted 
for.  Progress  consists  in  alternate  advancements  toward  com- 
pleteness along  both  lines,  from  both  directions. 
5  See  Sigwart,  Loyic,  Part  III,  chap.  vi. 


EXPLANATION 

Specific  Explanation. — But  in  practical  life  and  in 
the  historical  sciences  we  are  concerned  with  the  con- 
crete individual  fact;  hence  propositions  which  deal 
with  general  properties  and  the  like  are  of  no  use  to 
us  unless  we  can  see  how  they  apply  in  the  particular 
case;  and  usually  we  cannot  see  that  unless  we  have 
independent  knowledge  of  the  attendant  circumstances. 
The  knowledge  of  the  single  fact  and  of  the  general 
law  under  which  it  falls  does  not  ordinarily  enable  us 
to  reconstruct  the  system;  our  knowledge  of  both  fact 
and  laws  is  too  incomplete  to  enable  us  to  get  a  specific 
explanation ;  and  a  general  explanation  is  not  sufficient 
as  a  guide  for  action. 

Suppose  that  the  fact  under  investigation  were  a 
criminal  act  of  some  sort;  the  object  of  the  prosecut- 
ing attorney  is  to  fix  the  responsibility  for  the  act.  In 
order  to  do  this  it  is  necessary  for  him  to  reconstruct 
the  circumstances  surrounding  the  doing  of  the  act. 
In  other  words,  he  must  build  up  the  system  of  con- 
crete facts  to  which  the  act  belongs.  A  Sherlock 
Holmes  might  be  able,  by  superior  powers  of  observa- 
tion, unusual  knowledge  of  the  laws  of  criminal  be- 
havior, and  so  on,  and  by  extraordinary  skill  in  bringing 
each  fact  observed  under  the  proper  law,  to  reconstruct 
the  whole  system  of  facts  without  reliance  upon  the 
testimony  of  others ;  but  ordinary  mortals  would  usu- 
ally find  it  necessary  to  collect  evidence  from  all  pos- 
sible sources,  and  then,  out  of  the  scattered  bits,  to 
restore  some  semblance  of  the  original  whole.  One 
fact,  sufficiently  described,  and  a  thorough  grasp  of  the 
principles  of  the  system,  might  be  enough ;  lacking  that, 


THE    APPLICATION    OF    SCIENCE 

as  'many  fragments  as  possible  must  be  collected,  and 
even  then  no  certain  result  might  be  reached. 

Knowledge  of  the  laws  alone  does  not  ordinarily 
suffice,  and  even  if  that  knowledge  were  complete  it 
might  be  possible  to  go  astray  in  applying  it.  The 
greatest  scientist  might  fail  in  the  attempt  to  give  a 
specific  explanation  of  a  concrete  fact  if  he  should  over- 
look the  circumstances  surrounding  the  fact.  Specific 
explanation  is  a  matter  for  the  application  of  science, 
and  theory  alone  is  proverbially  insufficient  as  a  guide 
for  practice,  no  matter  how  correct  the  theory  may  be 
in  the  abstract.  The  "  theorist  "  may  have  an  incorrect 
theory  or  he  may  fail  to  note  the  special  circumstances 
in  applying  one  which  is  correct. 

Closely  related  to  the  processes  of  explanation  are 
those  of  prediction.  They  are  complementary.  In 
explaining,  we  give  the  laws  and  circumstances  which 
account  for  a  fact  or  a  supposed  fact ;  in  prediction 
we  set  out  from  a  set  of  laws  and  circumstances  and 
attempt  to  show  that  a  certain  fact  will  occur  in  the 
future  or  will  be  found  on  further  investigation  to 
exist.  Successful  prediction  is,  as  we  have  seen  in 
studying  the  inductive  methods,  a  test  of  the  validity 
of  the  laws  we  are  employing.  If  we  do  not  know  the 
laws  and  circumstances  we  can  not  predict  successfully, 
except  occasionally  and  by  accident.  Prediction  may 
be  said  to  represent  the  practical  application  of 
science. 


CHAPTER  II 
HYPOTHESIS 

What  is  an  Hypothesis? — Before  we  go  on  to  the 
discussion  of  certain  typical  systems,  it  is  necessary  to 
give  some  attention  to  another  matter  involved  in  most 
explanations,  namely,  the  use  of  hypotheses.  The 
term  hypothesis  is  used  in  several  different  senses,  but 
for  our  purposes  an  hypothesis  is  a  provisional  explan- 
ation. Fictions  made  for  the  purpose  of  argument, 
illustration,  or  simplification  may  also  be  regarded  as 
hypotheses,  but  we  shall  use  the  term  in  the  narrower 
sense.1 

Hypotheses,  or  provisional  explanations,  may  assert 
the  existence  of  a  fact,  as  when  we  assume  that  a  de- 
fective flue  was  the  cause  of  a  fire ;  or  of  a  law,  as 
when  we  infer  a  causal  connection  between  vaccination 
and  freedom  from  smallpox ;  or  of  a  complex  system 
of  laws  and  facts,  as  when  we  infer  the  existence  of  a 
matriarchal  system  in  the  early  history  of  certain 
peoples.  Inductive  inferences,  which  were  discussed  in 
chapter  vi.,  would  fall  under  the  head  of  hypotheses. 

The  Value  of  Hypotheses. — There  has  been  much 
disagreement  regarding  the  value  of  hypotheses  and 
their  use  in  science.  A  good  many  scientists  have  de- 
clared that  hypotheses  are  not  only  unnecessary  but 

i  For  an  interesting  discussion  of  the  subject,  see  Muir- 
head,  Philosophy  and  Life,  Art.  "  Hypothesis." 

246 


OPPOSITION  TO  USE  OF  HYPOTHESES 

are  positively  harmful,  and  Newton's  "  Hypotheses 
non  fingo  "  is  often  quoted  in  defense  of  their  position. 
To  apply  this  literally  would  mean  that  a  science  would 
remain  merely  a  body  of  carefully  observed  and  classi- 
fied facts,  unless  laws  should  somehow  or  other  spring 
ready  made  from  them  without  having  been  previously 
put  forward  as  possible  laws  and  then  tested  by  further 
observation  and  experiment.  Now,  it  might  sometimes 
be  possible  to  collect  our  facts  over  a  very  wide  range 
and  classify  them  and  their  relations  in  such  a  way 
as  to  show  at  once  the  law  of  their  connections ;  the 
inductive  methods  indicate  the  sort  of  grouping 
that  would  be  necessary ;  but  even  with  their  assistance 
it  would  rarely  happen  that  a  fully  verified  law  would 
appear  without  previous  unsuccessful  attempts  at  its 
discovery.  Previous  to  the  Nineteenth  Century  the 
progress  of  science  was  seriously  retarded  by  what 
Romanes  has  called  the  Bugbear  of  Speculation.  In  the 
introduction  to  his  Darwin  and  after  Darwin  he 
gives  the  following  statement  of  the  situation  in  the 
natural  sciences :  "  Fully  awakened  to  the  dangers  of 
web-spinning  from  the  ever  fertile  resources  of  their 
own  inner  consciousness,  naturalists  became  more  and 
more  convinced  that  their  science  ought  to  consist  in 
a  mere  observation  of  facts,  or  tabulation  of  phe- 
nomena without  attempt  at  theorization  upon  their 
philosophical  import.  If  the  facts  and  phenomena  pre- 
sented any  such  import,  that  was  an  affair  of  the  man 
of  letters  to  deal  with ;  but  as  men  of  science,  it  wras 
their  duty  to  avoid  the  seductive  temptations  of  the 
world,  the  flesh  and  the  devil,  in  the  form  of  specula- 
tion, deduction,  and  generalization  .  .  .  this  was  the 


248  HYPOTHESIS 

orthodox  and  general  view."  It  was  current  in  the 
time  of  Linnseus  and  even  to  the  time  of  Cuvier.  "  The 
Origin  of  Species  made  an  epoch  .  .  .  Darwin  dis- 
played the  true  principle  which  ought  to  govern  bio- 
logical research  ...  he  never  loses  sight  of  the  dis- 
tinction between  fact  and  theory  .  .  .  but  his  idea  of 
the  scientific  use  of  facts  is  plainly  that  of  furnishing 
legitimate  material  for  the  construction  of  theories 
.  .  .  the  spirit  of  speculation  is  the  same  as  the  spirit 
of  science,  namely,  to  know  the  causes  of  things  .  .  . 
If  it  be  causes  or  principles  as  distinguished  from  facts 
or  phenomena,  that  constitute  the  final  aim  of  scientific 
research,  obviously  the  advancement  of  such  research 
can  be  attained  only  by  the  framing  of  hypotheses. 
And  to  frame  such  hypotheses  is  to  speculate."  Dar- 
win said  of  himself  that  he  made  an  hypothesis  on  every 
subject.  "  He  was  as  productive  of  hypotheses  as 
nature  is  of  living  things,  and  like  her,  he  subjected 
them  all  to  the  principle  of  natural  selection."  2 

Hypotheses  are  necessary  for  science.  "  All  science 
starts  with  hypotheses,  in  other  words,  with  assump- 
tions that  are  unproved,  while  they  may  be  and  often 
are  erroneous;  but  which  are  better  than  nothing  to 
the  seeker  after  order  in  the  maze  of  phenomena."  3 

An  erroneous  hypothesis  may  be  quite  as  effective 
in  the  field  of  practical  activity  as  a  true  one  could  be. 
"  The  theory  that  some  god  would  destroy  the  tribe  if  it 
did  not  wash  at  a  particular  time  was  a  very  crude  ex- 
planation of  an  observed  fact ;  but  it  nevertheless  has 
its  merits.  It  caused  the  tribe  to  wash  occasionally — - 

2  Cramer,  The  Method  of  Darwin,  p.  40. 

3  Huxley,  Hume,  p.  65. 


MISTAKEN    HYPOTHESES  249 

a  thing  it  would  never  have  done.  It  furnished  a 
theory  which  tended  to  prevent  disease.  It  recognized 
the  truth  which  bacteriological  science  has  only  just 
grown  up  to  in  the  present  generation :  that  the  pen- 
alty for  violation  of  law  was  visited  not  so  much  on 
the  individual  as  on  the  community.4 

The  Ptolemaic  System  was  an  erroneous  hypothesis, 
but  without  it,  or  some  other  theory,  astronomical 
knowledge  would  have  progressed  much  more  slowly 
than  it  did.  "  The  superiority  of  the  Greeks  to  their 
Oriental  neighbors  in  science  has  often  been  accounted 
for  by  their  fertility  in  theory.  The  Oriental  peoples 
were,  at  the  time  of  which  we  write  (Cosmological 
Period),  considerably  richer  than  the  Greeks  in  accu- 
mulated facts,  though  these  facts  had  certainly  not 
been  observed  for  any  scientific  purpose,  and  their  pos- 
session never  suggested  a  revision  of  the  primitive  view 
of  the  world."  5 

The  danger  in  using  hypotheses  lies  in  the  fact  that 
we  are  so  likely  to  forget  that  they  are  only  hypotheses. 
We  find  some  explanation  which  seems  to  fit  the  facts 
or  which  supports  some  other  belief  of  ours,  and  we 
forget  that  our  hypothesis  has  not  been  verified.  We 
tend  to  have  too  great  a  fondness  for  hypotheses  which 
we  have  ourselves  made ;  we  are  liable  to  "  the  partiality 
of  intellectual  parentage."  Darwin's  example  may 
again  be  cited  as  the  right  one.  "  I  have  steadily  en-' 
deavored  to  keep  my  mind  free  so  as  to  give  up  any 
hypothesis,  however  much  beloved  (and  I  cannot  resist 

4  President  Hadley,  in  an  article  in  the  Atlantic  Monthly,  Feb*> 
ruary,  1903,  p.  153. 

5  Burnet,  Early  Greek  Philosophy,  1st  Ed.,  p.  22. 


250  HYPOTHESIS 

forming  one  on  every  subject),  as  soon  as  the  facts 
are  shown  to  be  opposed  to  it.  Indeed,  I  have  had  no 
choice  but  to  act  in  this  manner,  for,  with  the  exception 
of  the  Coral  Reefs,  I  cannot  remember  a  single  first- 
formed  hypothesis  which  had  not  after  a  short  time 
to  be  given  up  or  greatly  modified."  6 

It  has  been  said  that  an  hypothesis  is  a  question.7 
When  we  form  an  hypothesis  our  attitude  should  be 
described  by  the  inquiry :  "  Is  this  the  true  explanation 
of  the  facts?  "  If  that  attitude  could  be  preserved  the 
danger  from  hypotheses  would  be  very  small.  We  often 
hear  of  "  working  hypotheses."  They  are  simply 
hypotheses  which  are  confessedly  unverified  but  valu- 
able as  a  basis  on  which  to  work  toward  an  explanation. 
There  may  be  many  degrees  of  verification,  from  the 
most  complete  to  the  most  imperfect ;  strictly  speak- 
ing, one  might  say  that  until  an  hypothesis  has  been 
proved  true  and  shown  to  be  a  law  (and  therefore  no 
longer  a  mere  hypothesis)  it  remains  a  working  hypo- 
thesis ;  but  in  ordinary  usage  this  term  is  used  to  de- 
scribe hypotheses  which  are  useful  but  in  no  sense 
established. 

One  way  of  holding  the  mind  open  to  the  fact  that  a 
given  hypothesis  is  not  to  be  trusted  too  far  would 
be  to  keep  before  us  a  number  of  different  rival  hypo- 
theses.8 

6  Life  and  Letters,  Vol.  I,  p.  83,  quoted  in  Cramer's  Method  of 
Darwin. 

i  Langlois  and  Seignobos,  Introduction  to  the  Study  of  History. 

8  This  method,  which  has  been  called  the  "  Method  of  Multiple 
Working  Hypotheses,"  has  been  recommended  as  promoting  thor- 
oughness, suggesting  lines  of  inquiry,  as  a  means  of  sharpening 
discrimination,  increasing  fertility  in  reasoning  processes,  etc. 
See  Chamberlain,  The  Method  of  Multiple  Working  Hypothesest 
Science.  Feb.  7.  1890. 


THE  DERIVATION  OF  HYPOTHESES    251 

How  are  Hypotheses  Suggested  to  Us? — We  have 
already  seen  that  the  groupings  of  facts  or  sequences 
such  as  we  use  in  applying  the  method  of  Agreement 
and  the  rest  lead  to  the  formation  of  inductive  hypo- 
theses. Indeed  (1)  any  sequence  may  do  this.  If  we 
notice  that  A  is  followed  by  B,  we  tend  naturally,  in 
the  absence  of  evidence  to  the  contrary,  to  believe  that 
the  second  will  always  follow  the  first.  The  statement 
that  these  two  are  universally  and  necessarily  -connected 
in  this  way  is  an  hypothesis  unless  or  until  further  ex- 
amination shows  that  the  statement  is  either  true  or 
false. 

(£)  ANALOGY. — A  second  9  source  of  hypothesis  is 
found  in  Analogy.  The  term  analogy  has  been  used  in 
a  good  many  different  senses.10  In  its  broadest  sense 
it  means  any  kind  of  resemblance.  An  inference  from 
analogy  is  inference  from  the  resemblance  of  two  cases 
in  certain  observed  points  to  their  resemblance  in  a  fur- 
ther particular  which  has  been  observed  in  only  one  of 
them.  For  example,  we  may  observe,  in  examining  the 
skulls  of  certain  extinct  animals,  that  they  all  have 
sharp  canine  teeth  and  rudimentary  molars ;  in  this 
respect  they  resemble  modern  carnivorous  animals; 
hence  we  infer  that  these  extinct  animals  were  carnivo- 
rous. Or  we  know  that  a  boy  who  is  ill  has  eaten  unripe 
fruit ;  we  infer  that  another  boy  who  shows  similar 
symptoms  has  been  guilty  of  a  similar  indiscretion. 
Inference  from  analogy  is  usually  to  some  particular 

9  A  third  source  of  hypotheses  is  found  by  Sigwart  in  the  Con- 
version   of   propositions.      For    example,   isosceles   triangles   have 
the   angles   at  the  base  equal.     Is  the   converse  true?    See  Sig- 
wart, Logic,  ii,  p.  83. 

10  See  Minto,  Logic,  p.  367. 


252  HYPOTHESIS 

fact  or  situation,  though  it  may  be  further  extended 
to  a  general  principle. 

Analogy  alone  is  notoriously  an  unsafe  guide;  but 
if  certain  general  rules  are  kept  in  mind  it  may  often 
be  employed  to  advantage. 

1.  If  two  sets  of  facts  resembled  each  other  in  only 
one  particular  or  in  very  few,  an  inference  as  to  their 
resemblance  in  another  particular  would  be  very  haz- 
ardous.    The  fact  that  two  men  were  born  in  the  same 
city  gives  no  ground  for  the  conclusion  that  one  will 
have  the  same  profession  as  the  other. 

2.  If  two  sets  of  facts  resembled  each  other  in  every 
particular  except  such  as  were  irrelevant,  the  inference 
would  be   safe.      Reasoning  by   analogy   in   geometry 
illustrates  this.    Again,  if  two  animals  were  alike  except 
in  color,  the  fact  that  one  was  carnivorous  would  be 
good  ground  for  believing  that  the  other  was  too. 

3.  In  so  far  as  two  things  or  two  sets  of  facts  dif- 
fered in  relevant  particulars  the  inference  would  be  of 
doubtful  value.    If  one  of  two  twins  had  been  educated 
in  one  way  and  the  other  in  a  different  way,  it  would 
not  be  safe  to  infer  that  one  would  be  interested  in  the 
things  in  which  the  other  was  interested. 

4.  If  one   of  two   similar  things  possessed  a  char- 
acteristic  inconsistent  with   a   characteristic   possessed 
by  the  other,  it  would  of  course  be  impossible  to  infer 
that  the  first  thing  possessed  the  latter  characteristic. 
If  A  is  a  singer  we  cannot  infer  that  his  twin  brother 
B  is,  if  the  latter  is  deaf  and  dumb. 

5.  If    the    points    of   resemblance    outnumbered    the 
points  of  difference,  we  should  have  more  reasons  for 
than  against  the  inference,  provided,  of  course,  that 


ANALOGY  253 

the  various  points  were  equally  important  in  determin- 
ing the  character  of  the  things  in  question.  As  a  mat- 
ter of  fact  they  never  are  of  equal  importance,  so 
that  the  relative  importance  of  the  various  character- 
istics should  be  taken  into  account;  a  difference  in 
health  would  count  more  against  equal  strength  in  two 
men  than  similarity  of  stature,  weight  and  age  would 
count  in  its  favor. 

6.  In  counting  resemblances  and  differences,  only 
those  which  are  independent  should  be  counted;  the 
fact  that  a  planet  possesses  atmosphere  and  that  it 
refracts  light  passing  near  its  surface  are  not  inde- 
pendent; to  count  these  as  two  points  of  likeness  when 
trying  to  find  ground  for  the  conclusion  that  one 
planet  resembled  another  in  any  particular  respect 
would  be  incorrect. 

In  practice  it  is  not  easy  to  say  just  what  char- 
acteristics are  relevant  or  to  be  sure  whether  two  points 
are  independent.11 

Analogy  may  be  employed  in  connection  with  other 
grounds  of  inference ;  for  example,  if  a  given  situation 
possesses  factors  which  are  partly  like  and  partly  un- 
like those  in  another  situation  we  might  sometimes  infer 
the  presence  in  the  second  of  some  further  character- 
istic possessed  by  the  first,  but  in  less  degree.  One 
man  might  exhibit  some  of  the  symptoms  exhibited  by 
another  who  was  known  to  have  taken  a  certain  "drug; 
we  might  infer  that  the  first  had  taken  a  smaller  quan- 
tity of  the  same  drug,  and  so  on. 

Requisites  of  a  Good  Hypothesis. — Having  made 
our  hypothesis  on  whatever  ground,  we  should  ask  our- 
11  See  Hothouse,  Theory  of  Knowledge,  page  289,  seq. 


254  HYPOTHESIS 

selves  whether  it  is  worthy  of  serious  consideration. 
To  put  the  question  in  its  usual  form,  What  are  the 
requisites  of  a  good  hypothesis? 

1.  In  the  first  place  it  must  serve  the  purpose  for 
which   it   is   made;   it   must   offer   an    explanation   for 
data   which   have  not   previously   been    explained    cor- 
rectly.      Sometimes    certain    other    explanations    may 
have  been  offered  and  found  insufficient ;  sometimes  the 
data  may  have  been  entirely  unexplained.   An  hypothe- 
sis which  does  not  connect  at  least  two  facts  hitherto 
not  properly  connected  is  worthless. 

2.  A  good  hypothesis  must,  of  course,  be  consistent 
with  itself  and  with  all  the  data  concerned.     It  is  some- 
times said  that  an  hypothesis  must  not  contradict  known 
laws;  if  there  are  laws  which  are  completely  verified, 
the  hypothesis  must  be  in  agreement  with  them. 

That  does  not  mean  that  an  hypothesis  must  not 
disagree  with  any  principles  which  have  been  hitherto 
accepted.  Such  reasoning  would  have  ruled  out  the 
Copernican  Hypothesis,  and  it  did,  as  a  matter  of  fact, 
lead  many  to  reject  that  theory.  Strictly  speaking, 
any  hypothesis  which  offers  a  consistent  account  of  the 
data  and  their  relations  has  a  claim  to  consideration. 
In  practical  life  we  are  often  warranted  in  neglecting 
new  theories  which  contravene  accepted  principles,  at 
least  until  they  have  been  shown  to  approach  in  value 
and  soundness  those  already  current ;  but  the  specialist 
in  any  field  is  .not  justified  in  rejecting  a  theory  simply 
on  the  ground  that  it  disagrees  with  those  he  has  held 
in  the  past.  It  is  his  duty  to  test  all  of  them. 

3.  An   hypothesis,   to   be   worthy   of   consideration, 
must  be  capable  of  verification.     If  data  for  its  verifi- 


REQUISITES    OF    HYPOTHESES         255 

cation  are  not  already  at  hand  they  must  at  least  be 
conceivable  and  their  discovery  must  be  within  the 
bounds  of  possibility.  Herodotus,  in  discussing  the 
various  theories  of  the  rise  of  the  Nile,  says  of  the  one 
which  connected  it  with  the  mythical  stream  of  Ocean: 
"  The  person  who  speaks  about  the  Ocean,  since  he  has 
transported  the  question  to  the  dominion  of  the  in- 
scrutable, does  not  admit  of  refutation."  12 

4.  Other  things  being  equal,  choose  the  simplest 
hypothesis. 

Making  hypotheses  involves  mental  activities  which 
go  beyond  perception  and  memory.  They  are  often 
discussed  under  the  heading  of  "  Imagination."  But 
imagination  in  this  sense  is  not  simply  imagination  in 
the  limited  sense  of  making  mental  pictures.  It  involves 
constructive  activities  often  of  a  highly  complicated 
sort.  As  "  creative  "  imagination  it  differs  from  that 
of  the  poet  in  that  it  does  not  have  to  do  necessarily 
nor  primarily  with  concrete  experiences.13 

EXERCISES. 

State  the  ground  of  the  hypothesis  in  each  of  the  follow- 
ing examples  and  estimate  the  value  of  the  hypothesis: 

1.  Geologists,  watching  at  what  rate  changes  are  occur- 
ring in  the  earth's  surface  at  the  present  time, — e.  g.,  mak- 
ing   of   valleys,    glacier    movements,    etc., — determine    the 
length  of  time  it  must  have  taken  to  produce  the  corre- 
sponding changes  during  the  so-called  geological  periods. 

2.  In  looking  at  the  pictures  in  an  art  gallery,  our  atten- 
tion is  specially  attracted  by  one  picture  whose  character- 
istics  impress  themselves   in  our  mind.     Years  afterward, 
in  another  country,  we  again  see  those  characteristics  in 
another  picture  and  we  feel  certain  that  both  pictures  are 
the  work  of  the  same  artist. 

12  Gomperz,  Greek  Thinkers,  Bk.  IIL  chap,  p    6 

13  Minto,  Logic,  pp.  335,  33G. 


256  HYPOTHESIS 

3.  Cutting    tools    have    edges    and    places    for    handles. 
These  flints  have  edges  and  places  for  handles;  they  are 
therefore,  cutting  tools. 

4.  Some  Northwest  Coast  Indians  after  seeing  and  hear- 
ing a  phonograph  for  the  first  time,  were  asked  what  they 
thought  it  was.     Their  answer  was  that  it  was  a  very  power- 
ful echo  which  the  white  man  controlled  by  means  of  a 
"  strong  medicine  "  or  magic. 

5.  The  theory  that  many  philologists  hold,  that  many  of 
the  languages  of  the  world  may  be  traced  back  to  a  common 
stock,   known    as    the    Aryan,    is    based    on    analogy.      In 
Persian,  Greek,  Sanscrit,  etc.,  several  very  simple  words, 
usually  verbs,  such  as  to  give  and  to  be,  are  found  to  have 
almost  identically  the  same  root,  from  which  resemblances 
the  common  descent  is  argued. 

6.  Certain  mountains,  which  have  large  deposits  of  ba- 
salt, contain  gold.   When  large  deposits  of  basalt  are  found 
ire  other  mountains,  we  may  suppose  that  they  also  contain 
gold.     If  gold  is  not  found,  tin  is.     There  seems  to  be  a 
relation  between  deposits  of  basalt  and  deposits  of  gold. 

7.  Noting    that    certain    substances    expand    when    they 
crystallize,   and  noting  also  that  certain   other  substances 
expand  when  heated,  I  might  infer  that  heat  causes  the  lat- 
ter substance  to  crystallize  and  hence  to  expand. 

8.  Since  ether  has  been  offered  as  the  medium  of  trans- 
mission of  light-waves,  and  since  some  forms  of  electricity 
are  forms  of  wave-motion,  we  might  say  that  ether  is  the 
medium  of  transmission  of  electricity. 

9.  The  U.  S.  is  a  republic  and  its  citizens  are  prosperous 
and  contented;  we  may  therefore  infer  that  if  Cuba  were  a 
republic,  her  citizens  would  be  prosperous  and  happy  too. 

10.  Hydrochloric  acid  turns  blue  litmus  paper  red;  sul- 
phuric acid  has  similar  properties,  and  we  may  infer  that 
it,  too,  will  turn  blue  litmus  paper  red. 

11.  Bones  resembling  those  of  an  elephant  were  found 
in  a  given4  locality.     We  conclude  that,  at  some  time   or 
other,  elephants  lived  in  this  locality. 

12.  Cotton    is    grown    in   the    U.    S.    in    a    moist,   warm 
climate  and  a  sandy  soil;  we  may  infer  that  Egypt,  which 
has  these  characteristics,  will  also  grow  cotton. 


CHAPTER    III 
TYPICAL    SYSTEMS    OF    KNOWLEDGE 

AN  examination  of  the  methods  employed  in  estab- 
lishing certain  typical  varieties  of  systems  of  knowledge 
may  help  to  make  clearer  the  complexity  of  knowledge 
and  the  relations  of  the  processes  involved  in  getting 
it.  Every  system,  as  we  have  seen,  contains  laws. 
Some  of  them  are  systems  of  laws  and  general  concepts ; 
others  include  also  concrete  facts.  Let  us  take  as  an  ex- 
ample of  the  first,  the  sort  of  system  which  is  to  be 
found  in  mathematics  or  mechanics ;  and  as  examples 
of  the  second,  the  system  of  related  facts  which  the 
historian  or  the  criminal  lawyer  aims  to  establish.  The 
other  sciences  lie  between. 

We  cannot,  in  our  present  discussion,  begin  at  the 
very  beginning.  We  must  grant  to  the  historian  and 
the  lawyer  the  generally  accepted  laws  of  human  be- 
havior, the  accepted  principles  of  science,  in  short,  the 
working  materials  of  his  science.  To  the  mathema- 
tician, we  must  grant  his  concepts  and  axioms  and 
postulates,  and  to  both  the  general  principles  of  scien- 
tific method.  We  wish  merely  to  see  how  each  employs 
these  principles,  what  his  method  is.  All  these  concepts 
and  principles  have  been  brought  to  light  in  the  course 
of  human  experience.  The  mathematician  employs 
chiefly  the  processes  of  analysis  and  deductive  reason* 
ing.  Observation,  testimony  and,  in  general,  the  means 


258     TYPICAL    SYSTEMS    OF    KNOWLEDGE 

for  knowing  the  concrete  are,  for  the  most  part,  left 
aside  in  his  work. 

The  Geometric  System. — Let  us  take  an  example  of 
scientific  method  as  it  appears  in  the  science  of  geome- 
try. Other  fields  of  mathematics  differ  from  this  in 
important  respects,  but  for  the  purposes  of  illustra- 
tion geometry  will  be  sufficiently  representative.  What 
is  the  starting  point  in  geometry  and  what  sort  of  sys- 
tem does  it  attempt  to  build?1  Geometry  starts,  not 
with  perceived  objects  as  the  natural  sciences  do,  but 
with  a  set  of  concepts  and  propositions.  Among  its 
concepts  are  those  of  point,  line,  magnitude,  equality, 
and  so  on.  Some  of  these  are  definable  in  terms  of  the 
others,  as  "  a  point  is  that  which  has  no  magnitude." 
There  remain,  however,  certain  concepts  which  are  inde- 
finable, viz.,  those  by  means  of  which  all  the  others  are 
defined.  Of  these  concepts  there  are  two  kinds :  con- 
cepts of  elements,  and  concepts  of  relations.  Besides 
these  concepts  geometry  has  among  its  data  certain 
propositions  which  express  the  relations  which  hold 
among  its  elements.  These  propositions  are  known  as 
axioms  and  postulates.2 

1  See  Oswald  Veblen,  Popular  Science  Monthly,  Vol.  LXVIII, 
Art.  "The  Foundations  of  Geometry";  and  Transactions  of  the 
American  Mathematical  Society,  Vol.  5,  No.  3,  Art.    "A  System 
of  Axioms  for  Geometry." 

2  No   clear   line   of  distinction  was   drawn  by  Euclid  between 
axioms  and  postulates.    Both  were  regarded  as  unproved  and  un- 
provable  propositions  which  must  be  admitted  as  true  by  every 
one  who  understood  them,  as  a  priori  truths.     At  the  present  day 
their  a  priori  character  is  very  widely  questioned,  but  they  are 
unprovable   in  that  they  can  not  be  deduced   from   any  simpler 
propositions.     One  way  of  distinguishing  them  was  to  define  the 
axioms  as  common  notions  and  the  postulates  as  geometrical  pre- 
mises   which  must  be  taken  for  granted.     But  the  line  was  not 
clearly  drawn  and  propositions  which  sometimes  appeared  as  pos* 
tulates  were  at  other  times  put  among  the  axioms. 


MATHEMATICAL    SYSTEMS  259 

As  an  axiom  we  may  cite  the  first  in  the  list: 
"  Things  which  are  equal  to  the  same  thing  are  equal 
to  one  another  " ;  and  as  a  postulate :  "  A  straight  line 
may  be  drawn  from  any  one  point  to  any  other  point." 
"  All  right  angles  are  equal  to  one  another  "  has  some- 
times been  classed  as  an  axiom  and  sometimes  as  a  pos- 
tulate. Euclidian  geometry  may  be  defined  as  "  a 
system  of  propositions  codifying  in  a  definite  way  our 
spatial  judgments."  Every  one  of  its  propositions 
can  be  deduced  from  its  axioms  and  postulates,  except- 
ing, of  course,  the  axioms  and  postulates  themselves. 
To  prove  any  proposition  we  have  simply  to  combine 
certain  concepts  and  propositions  into  a  coherent 
whole. 

Let  us  examine  Proposition  XV,  Book  I.  "  Where 
two  straight  lines  (AB,  CD)  intersect  each  other,  the 
vertically  opposite  angles  made  by  them,  are  equal." 


The  demonstration  is  as  follows :  "  For  the  angk 
CFA  +  the  angle  AFD  =  two  right  angles  (prop.  13), 
and  also  the  angle  AFD  +  the  angle  DFB  =  two  right 
angles ;  therefore  the  angle  CFA  -f  the  angle  AFD  = 
the  angle  AFD  +  the  angle  DFB  (axiom  1)  ;  and  the 
common  angle  AFD  being  taken  away  from  both,  there 
remains  the  angle  CFA  =  the  angle  DFB  (axiom  3)  ; 
but  these  are  vertically  opposite  angles.  In  like  man- 
ner it  may  be  proved  that  the  vertically  opposite  angles 


260    TYPICAL    SYSTEMS    OF    KNOWLEDGE 

AFD  and  BFC  are  equal."  What  are  the  concepts 
and  propositions  employed  in  the  proof  of  this  theorem? 
We  have  concepts  of  number  (two,  e.  g\),  straight 
lines,  point,  circle,  intersection,  angles,  right  angles, 
vertically  opposite  angles,  equality,  addition,  subtrac- 
tion, remainder,  etc. 

We  employ,  among  the  propositions,  Proposition 
XIII  (When  a  straight  line  standing  upon  another 
straight  line  makes  angles  with  it  they  are  either  two 
right  angles  or  together  equal  to  two  right  angles)  ; 
this  proposition  was  proved  from  certain  others  all 
resting  ultimately  upon  the  axioms  and  postulates.  We 
employ  Postulate  3  (A  circle  may  be  described  from 
any  center,  with  any  interval  from  that  center)  ;  Postu- 
late 1  (A  straight  line  may  be  drawn  from  any  one 
point  to  any  other  point)  ;  Definition  12  (A  circle  is  a 
plane  figure  bounded  by  one  line  called  the  circumfer- 
ence or  periphery ;  to  which  all  straight  lines  drawn 
from  a  certain  point  within  the  figure,  are  equal)  ;  also 
Axiom  1  (Things  which  are  equal  to  the  same  thing 
are  equal  to  each  other). 

Geometrical  demonstrations  are  made  with  reference 
to  figures,  and  it  might  seem  as  if  we  were  really  dealing 
with  a  concrete  particular  case  instead  of  with  general 
concepts  alone ;  but  the  concrete  case  is  simply  an 
illustration  and  the  whole  demonstration  is  absolutely 
general.  Accurate  measurements  of  the  figure  would 
undoubtedly  show  inequalities  between  the  vertically 
opposite  angles  for  the  reason  that  the  lines  are  not 
absolutely  straight;  the  figure  symbolizes  the  intersec- 
tion of  any  two  absolutely  straight  lines  and  the  dem- 
onstration is  true  of  all  such  lines  and  only  of  such. 


PURE    SCIENCES 

Similar  statements  apply  to  all  the  figures  used  in  dem- 
onstrating geometrical  propositions.  Euclidian  geom- 
etry as  a  whole  is  simply  a  complex  system  built  up  in 
the  manner  illustrated  by  the  example  above. 

The  data  of  the  geometrician  are  comparatively  few 
and  simple.  His  general  principles  are  already  deter- 
mined ;  his  tests  of  truth  are  agreement  with  his  prin- 
ciples, and  not  absolute  agreement  with  concrete  fa-cts ; 
however,  he  believes  that  if  it  were  possible  to  observe 
and  measure  the  facts  accurately,  and  if  facts  could 
be  found  to  agree  with  his  definitions  of  straight  line, 
circle,  etc.,  for  example,  his  conclusions  would  be  found 
in  correspondence  with  them.3 

The  system  which  we  have  just  examined  aims  at  the 
organization  of  a  set  of  judgments  having  a  general 
application  and  not  with  any  specific  data.  The  science 
of  geometry  is  not  interested  in  this  or  that  geometrical 
figure ;  it  gives  us  information  regarding  figures  of 
certain  kinds,  leaving  the  question  of  its  application 
to  particular  cases  to  the  applied  sciences.  All  of  the 
so-called  "pure  sciences"  are  like  geometry  in  this  re- 
spect. They  deal  with  general  principles,  not  with 
particular  cases.  Sometimes  the  arts  and  sciences  are 
distinguished  along  this  line,  the  arts  being  defined  as 
the  application  in  practice  of  the  principles  embodied 
in  the  sciences.  The  science  of  geometry  is  a  system 
founded  upon  a  certain  few  general  principles  which 
are  described  as  axiomatic. 

Most  of  the  sciences  include,  besides  axiomatic  prin- 

s  Recently,  other  systems  of  geometry  have  been  built  up.  The 
methods  employed  are  the  same  as  those  of  Euclidian  geometry, 
but  they  assume  different  postulates.  The  only  requirement-  is 
that  the  system  built  upon  them  shall  be  a  coherent  whole. 


262    TYPICAL    SYSTEMS    OF    KNOWLEDGE 

ciples,  others  which  are  the  outcome  of  the  application 
of  the  methods  of  science  to  the  study  of  empirical 
data.  The  science  of  Mechanics  is  an  example  of  this. 
As  we  have  seen,  it  "  lays  down  propositions  which  are 
true  in  the  same  way  of  all  fluids,  all  gases,  etc." 
These  laws  were  discovered  as  a  result  of  a  multitude 
of  observations  of  the  behavior  of  particular  bodies  of 
fluid,  gas,  etc. ;  the  observations  were  recorded, 
classified  and  made  the  basis  of  inductive  inferences, 
which  were  tested  as  completely  as  possible.  Hence 
all  the  processes  included  in  the  scientific  method  of  es- 
tablishing laws  are  employed,  but  strong  emphasis  is 
placed  upon  the  establishment  of  further  conclusions 
on  the  basis  of  these  laws,  in  other  words,  the  deductive 
part  of  scientific  method  is  emphasized. 

Somewhat  similar  statements  may  be  made  regarding 
the  science  of  Chemistry,  though  chemistry  is  perhaps 
less  independent  of  particular  facts  and  less  able  to 
proceed  deductively  on  the  basis  of  generalizations  al- 
ready established ;  and  certain  departments  of  chem- 
istry are  concerned  rather  with  the  classification  of 
facts  than  with  attempts  to  found  a  deductive  science. 
Observation,  analysis,  classification  and  induction  are 
all  employed.  Still,  even  in  chemistry  there  is  much 
that  is  deductive,  and  the  interest  of  the  chemist  in 
particular  facts  tends  to  become  only  indirect. 

Biology  and  Psychology  may  also  be  mentioned  at 
this  point.  Both  are  interested  in  concrete  phenomena 
mainly  for  the  sake  of  the  general  conclusions  which 
may  be  based  upon  them.  Both  employ  the  whole  of 
scientific  method,  including  the  use  of  statistics,  aver- 
ages and  probability.  Both  are  farther  than  chemis' 


PSYCHOLOGY    AND    BIOLOGY          263 

try  from  the  point  at  which  a  science  begins  to  be 
primarily  deductive.  The  employment  of  statistics 
and  of  methods  of  exact  measurement  has  become  of 
very  great  importance  in  these  two  sciences  within  the 
past  few  years.  Reference  to  the  recent  literature  of 
both  subjects  makes  this  very  evident.  As  examples  in 
psychology  we  might  cite  studies  of  animal  behavior 
and  studies  in  child  psychology ; 4  in  biology,  the  in- 
vestigations connected  with  Mendel's  Law,  the  study 
of  Variation,  and  so  on.5 

The  pages  from  the  works  of  Professor  James  (pages 
280-284),  illustrate  psychological  analysis,  which  docs 
not  employ  statistics ;  and  the  essay  from  Huxley's 
works  (pages  287-300)  illustrates  the  same  thing  in 
the  field  of  biology.  Neither  passage  can  be  regarded 
as  representative  of  the  studies  which  are  most  fre- 
quent at  the  present  time.  Both  are  exceptionally 
broad  in  scope  and  deductive  in  character,  but  both 
do  illustrate  the  desire  of  scientists  in  both  fields  to 
arrive  at  general  conclusions  and  to  establish  coherent 
systems. 

Systems  Which  are  More  Concerned  with  Concrete 
Data. — We  wish  now  to  consider  systems  which  have 
to  do  with  concrete  data  in  a  different  way ;  systems 
which  give  to  specific  instances  their  exact  place  in  a 
system  of  concrete  facts ;  systems  which  not  only  pre- 
sent a  body  of  general  laws,  but  also  apply  them  to  the 
explanation  of  specific  cases ;  systems  which  state  com- 
pletely the  causes  of  given  phenomena  or  enable  us  to 

4  See  Yerkes,  The  Dancing  Mouse;  Washburn,  The  Animal 
Mind;  Thorndike,  Educational  Psychology;  and  articles  in  jour- 
nals. 

o  See  Punnett,  Mendelivm;  and  articles  in  journals. 


264    TYPICAL    SYSTEMS    OF    KNOWLEDGE 

establish   the   existence   of   given   events    or   situations 
not  at  present  open  to   observation. 

History,  in  so  far  as  it  is  concerned  with  the  recon- 
struction of  the  past,  is  a  case  in  point ;  so  also  is  the 
criminal  lawyer's  attempt  to  discover  the  individual 
guilty  of  a  crime ;  again  Geology,  when  it  aims  at  the 
discovery  of  past  changes  and  conditions  of  the  earth 
falls  in  the  same  class.  In  geology  the  primary  data 
are  almost  entirely  the  present  character  of  the  earth's 
surface  and  the  changes  which  are  constantly  going 
on.  It  includes,  of  course,  many  of  the  data  and  con- 
clusions of  physics,  chemistry,  and  biology.  On  the 
basis  of  these  data  it  is  able  to  arrive  at  well-founded 
conclusions  concerning  changes  which  never  could  have 
been  observed.  It  assumes,  as  does  all  science,  that 
unless  there  is  evidence  to  the  contrary,  the  past  and 
the  unobserved  are  like  the  present  and  the  observed. 

"  Many  of  the  changes  which  have  indisputably  taken 
place  are  such  as  no  man  has  ever  observed,  because 
they  are  brought  about  so  slowly  or  so  deep  down 
within  the  crust  that  no  direct  observation  is  pos- 
sible, and  we  can  only  infer  the  mode  of  procedure  by 
examining  the  result.  No  human  eye  has  ever  witnessed 
the  birth  of  a  mountain  range,  or  has  seen  the  beds 
of  solid  rock  folded  and  crumpled  like  so  many  sheets 
of  paper,  or  observed  the  processes  by  which  rock  is 
changed  in  all  its  essential  characteristics ;  '  metamor- 
phosed '  as  it  is  technically  called."  6  Conclusions  of 
this  character  imply  the  existence  of  a  well  organized 
body  of  knowledge  concerning  the  relations  of  facts 
in  the  given  field. 

o  Scott,  Introduction  to  Qeology,  p.  30, 


ASTRONOMY  265 

The  data  of  the  science  were  obtained  by  observation ; 
the  facts  observed  were  classified  and  correlated ;  laws 
were  gradually  discovered  and  verified ;  systems  were 
constructed  and  rejected  until  eventually  a  set  of  gen- 
eral principles  emerged  upon  which  geologists  could 
agree;  but  the  working  out  of  the  details  and  the  ex- 
position of  the  system  of  concrete  facts  involved — 
in  other  words  the  history  of  the  earth — has  progressed 
only  a  little  way.  In  geometry  observation  is  only 
incidental ;  in  any  concrete  science  it  is  a  constant  neces- 
sity. In  a  historical  science  the  particular  fact  occu- 
pies the  center  of  the  field;  in  other  sciences  the  pri- 
mary interest  is  in  generalizations. 

The  discovery  of  the  planet  Neptune  implied  the 
construction  of  a  similar  system  -in  Astronomy.  The 
planets  move  in  elliptical  orbits;  these  orbits,  how- 
ever, are  not  perfect  ellipses ;  there  are  variations  (per- 
turbations) due  to  the  influence  of  other  planets.  The 
amount  of  variation  due  to  any  planet  can  be  calcu- 
lated. In  the  case  of  the  planet  Uranus,  after  all  the 
perturbations  due  to  the  known  planets  had  been  taken 
into  ac-count,  there  remained  a  residue  unaccounted  for. 
Adams  and  Leverrier  calculated  that  this  residue  could 
be  accounted  for  by  the  hypothesis  of  another  planet 
in  a  given  direction  and  at  a  given  distance  from 
Uranus ;  and  this  planet  was  soon  after  discovered  with 
the  aid  of  the  telescope  and  was  named  Neptune.  The 
discovery  of  Neptune  presupposed  a  knowledge  of  the 
general  laws  of  the  solar  system  and  a  comprehensive 
description  of  the  relation  in  which  its  known  mem- 
bers stood  to  each  other.  It  was  the  result  of  the  ap- 
plication of  the  general  laws  to  a  concrete  situation. 


266     TYPICAL    SYSTEMS    OF    KNOWLEDGE 

Systems  of  Historical  Facts. — Both  astronomy  and 
geology  find  a  large  part  of  the  concrete  data  with 
which  they  deal  open  to  observation;  geology  to  some 
extent  and  astronomy  to  a  great  extent  depend  upon 
the  testimony  of  past  observers.  In  the  courts  and  in 
the  investigations  of  the  historian,  testimony  is  of  the 
first  importance.  We  may  then  classify  the  data  in 
these  investigations  as  follows : 

1.  Material  facts. 

£.  Testimony. 

Examples  of  material  facts  would  be  the  articles 
found  on  the  scene  of  the  crime,  etc.,  etc. ;  and  in 
historical  inquiries,  the  ruins  of  buildings,  roads,  and 
other  public  works,  tombs,  ancient  implements,  works 
of  art,  etc.,  etc.  The  testimony  may  be  either  oral 
or  written.  Usually  the  historian  must  rely  princi- 
pally upon  written  testimony.  It  is  of  many  kinds, 
from  the  pictographs  of  primitive  man  to  historical 
accounts  like  those  of  Thucydides  and  Tacitus.  The 
problems  of  the  historian  are  to  collect  the  data,  weigh 
the  value  of  each  of  the  items,  and  construct  an  account 
which  will  best  organize  the  data  into  a  coherent  whole. 

A.  His  first  duty  will  be  to  collect  all  the  data  pos- 
sible. The  methods  employed  by  the  lawyer  are  suffi- 
ciently familiar  in  their  general  outlines.  Details  of 
his  methods  are  beyond  the  scope  of  our  discussion. 
We  shall  consider  the  procedure  of  the  historian  a 
little  more  closely.  He  must  search  for  documents. 
"  Documents  are  traces  which  have  been  left  by  the 
thoughts  and  actions  of  men  of  former  times"  7  whether 

1  Langlois  and  Seignobos,  Introduction  to  the  Study  of  History. 
This  is  a  most  valuable  introduction  to  the  method  of  history  and 
should  be  read  by  every  student  of  scientific  method. 


HISTORY  267 

material  facts,  such  as  works  of  art  and  the  like,  or 
written  records.  Some  historians  have  described  events 
so  recent  that  it  was  possible  to  obtain  the  testimony 
of  eye-witnesses.  They  were  thus  able  to  obtain  a 
quantity  of  testimony  not  available  for  the  later  writer 
and  to  cross-examine  their  witnesses.  Usually  the  dis- 
covery of  documents  has  meant  a  search  in  all  sorts  of 
places  for  the  testimony  of  contemporaries ;  the  ex- 
peditions and  excavations  carried  on  by  the  archaeolo- 
gists have  as  their  object  the  discovery  of  such  records. 
Archives,  state  papers,  early  histories,  memoirs,  in- 
scriptions, etc.,  furnish  the  chief  sources.  The  problem 
grows  easier  with  the  growth  of  collections  and  li- 
braries. But  new  documents  are  constantly  being 
found,  and  no  one  can  say  when  the  data  have  all  been 
discovered. 

B.  After  the  collection  of  the  data  comes  the  esti- 
mation of  the  value  of  its  various  items.  Estimating 
the  value  of  testimony  is  a  special  problem  and  we 
shall  treat  of  it  first.8  The  problem  is  to  discover 
what  facts  the  documents  establish.  The  questions  to 
be  raised  are  such  as  these:  Who  did  such  and  such  an 
act?  Who  wrote  such  and  such  a  poem?  Who  founded 
Rome?  The  answer  involves  the  establishment  of  a 
system  of  facts  and  inferences  justifying  some  one 

conclusion  to  the  exclusion  of  all  others.    The  establish- 

• 

ment  of  such  a  system  means  the  discovery  of  facts, 
their  classification,  the  construction  of  hypotheses,  and 

s  Estimating  the  value  of  testimony  is  so  important  a  matter 
in  inquiries  of  the  sort  we  are  now  considering  that  the  questions 
involved  will  be  discussed  somewhat  more  fully  than  in  the  intro- 
ductory chapter.  All  the  machinery  of  scientific  method  may  be 
needed  to  enable  the  historian  to  decide  whether  or  not  a  record 
is  trustworthy. 


268    TYPICAL    SYSTEMS    OF    KNOWLEDGE 

the  'verification  of  these,  and  the  organization  of  facts 
and  generalizations  into  a  system.  We  know  facts  by 
observation,  by  memory  aided  by  inference,  by  infer- 
ence from  the  testimony  of  others,  by  inference  from 
remains  of  former  human  activities,  and  from  all  sorts 
of  natural  events,  and  natural  processes ;  we  group  the 
data  with  reference  to  their  bearing  on  various  parts 
of  the  problem ;  we  use  the  inferences  based  upon  past 
experience  and  formulate  new  ones ;  we  test  our  con- 
structions by  all  known  means. 

Sometimes  observations  of  natural  phenomena  may 
make  up  most  of  the  data.  Observations  made  by  others 
may  sometimes  be  easily  verified.  Experiments  may 
be  repeated ;  the  problem  of  getting  correct  descrip- 
tions of  the  facts  may  frequently  be  comparatively 
easy.  But  the  sort  of  case  which  illustrates  the  estab- 
lishment of  a  system  of  concrete  facts  in  all  its  com- 
plexity is  that  in  which  human  testimony,  as  well  as  all 
other  kinds  of  data  is  employed  to  determine  the 
existence  and  character  of  some  fact.  Let  us  examine 
in  outline  the  processes  involved  in  guarding  against 
error  in  the  use  of  testimony.  A  number  of  pre- 
liminary questions  must  be  raised: 

(1)  The  first  of  them  is  this :  What  is  the  testimony? 
What  does  the  witness  say?  What  is  the  content  of 
the  document.  The  testimony  ^  the  starting  point. 
We  must  know  what  the  words  mean,  what  they  pur- 
port to  tell,  what  facts  they  are  intended  to  represent. 
(a)  In  the  case  of  the  witness  on  the  stand  this  ques- 
tion, though  all-important,  is  usually  comparatively 
easy  of  solution.  In  case  of  doubt  he  can  be  called 
upon  for  further  statements,  which  will  make  plain  his 
meaning.  When  he  speaks  in  a  foreign  language  there 


HISTORY  269 

Is  more  difficulty,  but  in  any  ordinary  description  of 
facts,  the  difficulty  is  not  great,  (b)  In  the  case  of 
historical  documents  the  difficulty  may  be  insurmount- 
able. For  centuries  hieroglyphics  could  not  be  inter- 
preted at  all ;  and  translations  from  ancient  documents 
are  always  attended  with  danger.  The  difficulty  of  find- 
ing in  one  language  exact  equivalents  of  the  words  of 
another  needs  no  emphasis.  In  such  a  case  the  most 
thoroughgoing  comparison  of  the  two  languages  may 
be  necessary  in  order  to  determine  the  meaning  of  a 
document.  Whole  sciences,  such  as  epigraphy  or  palae- 
ography, are  devoted  to  the  interpretation  of  ancient 
writings. 

(2)  If  the  meaning  of  the  statements  contained  in 
the  testimony  has  been  made  clear,  the  next  question 
is,  of  course:  Are  the  statements  true?  And  in  order 
to  answer  this  we  may  ask  next:  («)  Who  made  the, 
statements,  and  is  he  qualified  by  knowledge,  honesty 
and  accuracy  sufficient  to  enable  us  to  rely  upon  what 
he  says?  In  the  law  courts,  the  identity  of  the  witness 
is  the  first  thing  to  be  determined  and  made  a  matter 
of  record.  When  the  witness  is  before  us  the  question 
of  his  identity  is  usually  very  easy  to  answer,  though 
there  are,  of  course,  numerous  cases  in  which  error  and 
deception  might  occur.  And  in  the  case  of  the  pris- 
oner, the  determination  of  identity  is  often  an  ex- 
tremely difficult  matter,  involving  testimony  and  many 
other  kinds  of  evidence. 

In  the  case  of  written  documents  the  determination 

of  authorship  is  one  of  the  most  difficult  problems  which 

the  historian  has  to  solve.9     The  name  upon  the  title 

page  of  a  book  is,  by  itself,  not  conclusive  as  evidence 

»  See  Langlois  and  Seignobos,  Book  II,  chap.  iii. 


270    TYPICAL    SYSTEMS    OF    KNOWLEDGE 

of  authorship.  In  modern  books  the  indications  of 
authorship  are  usually  fully  given  and  are  ordinarily 
reliable;  fraud  is  possible,  but  is  usually  easily  de- 
tected, though  forgeries  in  the  name  of  dead  authors 
may  be  successful.  But  in  the  case  of  early  books,  and 
above  all  in  the  case  of  manuscripts,  the  difficulties  are 
very  great ;  in  the  first  place  there  may  be  no  formal 
indications  of  authorship;  or  the  work  is  perhaps 
ascribed  to  such  and  such  a  person.  Was  he  the  author? 
We  should  ask  first:  Did  such  a  person  ever  exist? 
To  answer  this,  only  the  testimony  of  contempo- 
raries would  be  conclusive.  In  many  cases  it  is  not 
necessary  to  pause  over  this  question,  for  there  may  be 
no  doubt  about  the  existence  of  the  author ;  but  in  case 
there  should  be,  the  testimony  to  his  having  existed 
must  be  tested  like  any  other  such  evidence.  Con- 
sistency of  testimony  and  corroboration  of  one  piece 
of  testimony  by  another  are  necessary  here  as  else- 
where. One  of  the  best  known  examples  of  this  problem 
is  that  of  the  existence  of  Homer.  Absence  of  testi- 
mony in  this  and  other  cases  is  usually  a  presumption 
against  the  truth  of  what  is  alleged. 

Granted  that  there  was  such  a  person  as  the  author, 

did  he  write  the  document  before  us?     What  evidence 

is   there   of  the   genuineness   of   the   document?      The 

evidence  is   of  two  kinds,  internal   and   external.     In 

examining    internal    evidence,    the    question     is :       Is 

the   document   such   as    the    alleged    author   could   or 

would  have  written?   Is  the  handwriting  of  a  sort  that 

was  employed  during  the  lifetime  and  in  the  country, 

*tc.,  of  the  supposed  author?    If  the  document  is  in 

Handwriting  of  the  Eleventh  or  the  Thirteenth  Century, 


INTERNAL  AND  EXTERNAL  EVIDENCE     271 

it  was  not  written  by  an  author  of  the  Twelfth  Century. 
And  with  regard  to  the  style  and  forms  of  expression 
the  same  question  may  be  raised.  In  legal  documents 
this  is  a  valuable  test,  for  legal  phraseology  is  very 
definite.  Modern  words  or  phrases  in  a  supposed  an- 
cient writing  are,  of  course,  conclusive  against  any 
argument  for  its  genuineness. 

Mention  of  facts  and  allusions  to  events  of  every 
sort  are  most  valuable  in  this  connection ;  and  lastly, 
the  opinions  expressed  or  implied  .in  the  document  are 
of  great  assistance  in  determining  its  genuineness,  for 
some  opinions  could  not  possibly  have  been  held  at  the 
time  the  document  purports  to  have  been  written.  Ex^ 
ternal  evidence  is  to  be  found  in  references  to  the 
document,  quotations,  etc.,  by  contemporaries  or  by 
those  of  later  periods. 

Another  complication  is  often  present  to  add  to  the 
difficulty  of  determining  authorship ;  the  document  may 
be  the  work  of  two  or  more  individuals,  or  changes  may 
have  been  introduced  by  those  who  have  edited  the 
texts,  or  there  may  have  been  mistakes  in  copying. 
In  all  these  cases  one  should  not  necessarily  reject  the 
work  as  a  whole;  it  may  give  some  information  and  we 
may  be  able  to  detect  the  changes  from  the  original, 
and  it  may  be  of  great  importance  to  determine  just 
what  was  done  by  the  original  author  or  just  what  was 
written  by  each  of  several  collaborators.  The  methods 
to  be  employed  are  of  course  those  described  above. 
It  is  simply  a  question  of  several  authors  instead  of 
one. 

(b)  Having  assured  ourselves  of  the  identity  of  the 
witness  or  witnesses,  the  next  question  is:  Was  he  in  a 


TYPICAL    SYSTEMS    OF    KNOWLEDGE 

position  to  know  the  facts  to  which  he  is  testifying? 
Does  he  assert  that  he  witnessed  them  himself?  10  And 
was  it  humanly  possible  for  any  one  to  have  observed 
the  facts  in  question?  And  if  this  question  can  be  an- 
swered in  the  affirmative,  we  have  next  to  ask  whether 
there  is  any  reason  why  the  witness  himself  could  not 
have  observed  them.  Was  he  (i)  competent  to  observe 
and  remember  the  facts?  Was  there  any  defect  in  his 
powers  of  observation,  or  is  there  any  evidence  against 
his  having  been  at  a  place  where  the  observation  could 
have  been  made?  Here  again,  when  we  have  the  wit- 
ness before  us,  the  difficulty  of  solving  the  problem  is 
much  easier  than  when  we  have  to  rely  upon  written 
testimony,  or  other  evidence  of  an  indirect  sort. 

Cross-examination  is  a  method  of  getting  at  once  an 
addition  to  the  testimony  on  the  points  already  raised 
and  of  furnishing  immediately  statements  which  will 
corroborate  or  disagree  with  statements  already  made, 
or  with  known  facts.  In  Lincoln's  first  murder  trial, 
the  chief  witness  had  testified  to  seeing  the  murder 
committed  by  the  prisoner.  In  the  cross-examination 
he  added  a  number  of  details :  that  the  shooting  was  at 
ten  o'clock  at  night,  in  beech  timber,  in  August,  that 
he  was  twenty  feet  or  more  away,  that  he  could  see  the 
pistol  and  how  it  hung;  that  the  nearest  lights  were 
half  a  mile  away,  and  that  he  saw  it  all  by  moonlight. 
Lincoln  showed  that  the  moon  did  not  rise  till  one 
o'clock  in  the  morning.  Cross-examination  may  bring 
out  inconsistencies  due  to  dishonesty  as  well  as  incom- 
petence, as  shown  in  this  example.  Where  cross-ex- 

10  As  Bain  asserts  (Logic,  Appendix  I),  "The  supreme  canon 
of  historical  evidence  is  testimony  of  a  contemporary  " — of  one 
who  may  have  observed  the  fact. 


TESTIMONY  273 

amination  is  impossible,  as  in  written  testimony,  it  may 
be  impossible  to  convict  a  dishonest  witness. 

(ii)  If  the  witness  has  withstood  all  the  preceding 
tests  we  have  next  to  ask  whether  there  is  anything  in 
his  record  which  would  lead  us  to  doubt  his  honesty  or 
whether  he  is  likely  to  have  any  reason  for  falsifying  in 
the  present  case.  The  two  questions  are  distinct;  a 
general  good  reputation  would  be  a  presumption  in 
favor  of  his  honesty  in  the  present  case,  but  it  would 
not  make  it  certain  that  he  was  proof  against  all  temp- 
tation. In  the  courts,  cross-examination  of  the  wit- 
ness himself  and  the  testimony  of  other  witnesses  fur- 
nish the  data  for  answering  the  question ;  in  written 
testimony,  other  statements  of  his  own  and  the  state- 
ments of  his  contemporaries  must  be  taken  into  ac- 
count; what  is  implied  is  often  more  important  than 
what  is  stated  outright. 

There  are  two  cases  in  which  the  testimony  of  a  wit- 
ness may  be  regarded  as  particularly  free  from  wilful 
falsification.  The  first  is  that  in  which  the  witness  be- 
lieves the  evidence  is  to  his  discredit  or  disadvantage. 
One  exception  must  be  made :  the  witness,  for  the 
sake  of  satisfying  a  grudge  or  shielding  someone  else, 
might  be  willing  to  sacrifice  his  own  reputation  and 
advantage.  In  any  case,  such  testimony  would  need 
further  corroboration,  but  it  would,  with  the  excep- 
tion above  mentioned,  be  excellent  evidence  of  the  good 
faith  of  the  witness. 

The  second  case  is  that  in  which  evidence  is  given 
undesignedly.  The  witness  makes  statements  of  whose 
import  he  is  unaware  or  he  is  surprised  into  statements 
which  bring  out  facts  which  he  has  been  attempting  to 


274    TYPICAL    SYSTEMS    OF    KNOWLEDGE 

conceal.      An   incident   related  in   Voltaire's   "  Zadig " 
will  illustrate  this: 


Zadig's  master,  Setoc,  had  lent  money  in  the  presence 
of  two  witnesses  who  had  died  before  the  debt  was  paid. 
The  debtor  denied  having  received  any  money.  The  money 
had  been  counted  out  upon  a  stone  near  Mount  Horeb. 
Zadig  undertook  to  conduct  the  case.  He  summoned  the 
debtor  before  a  tribunal  and  demanded  that  the  five  hun- 
dred ounces  of  silver  be  returned  to  his  master.  "  Have  you 
witnesses?  "  asked  the  judge.  "  No/'  replied  Zadig,  "  they 
are  dead;  but  there  is  a  large  stone  on  which  the  money 
was  counted  out;  if  it  please  Your  Highness  to  order  that 
the  stone  be  sought  out,  I  hope  that  it  will  bear  witness; 
the  debtor  and  I  will  remain  here  until  the  stone  arrives; 
I  will  have  it  hunted  up  at  the  expense  of  my  master." 
"  Very  well,"  replied  the  judge,  and  he  turned  his  atten- 
tion to  something  else.  At  the  end  of  the  sitting  he  said 
to  Zadig,  "Well,  your  stone  has  not  yet  arrived?"  The 
debtor  laughed  and  said:  "  If  your  Highness  should  re- 
main here  till  to-morrow  the  stone  would  not  have  arrived; 
it  is  more  than  six  miles  away  and  it  would  require  fifteen 
men  to  move  it."  "  Well,"  cried  Zadig,  "  I  told  you  that 
the  stone  would  bear  witness;  since  this  man  knows  where 
it  is,  he  admits  that  it  was  upon  it  that  the  money  was 
counted  out." — Voltaire,  Zadig,  Chap.  x. 

Testimony  which  is  false  is  of  course  evidence  of 
something, — of  the  opinion  of  the  witness,  or  of  his 
character,  or  of  the  existence  of  certain  ideas,  etc.,  at 
the  time  in  which  he  lived. 

But  all  these  questions  are  more  or  less  preliminary. 
A  witness  of  good  reputation  and  a  good  observer, 
with  no  motive  to  falsify,  may,  of  course,  be  mistaken 
in  the  case  under  examination.  And  a  witness  who  is 
not  usually  reliable  or  who  is  a  bad  observer  or  one  with 
every  reason  to  falsify,  may  be  telling  the  truth.  In  the 


TESTIMONY  275 

first  case  the  presumption  would  of  course  be  in  favor 
of  the  testimony  and  in  the  second  against  it,  but  in 
neither  case  could  we  regard  the  reliability  of  the  testi- 
mony as  settled.  There  are  three  conditions  to  the  ac- 
ceptance of  every  piece  of  testimony.  (1)  It  must  bq 
self-consistent  and  internally  coherent;  (2)  it  must  be 
consistent  and  coherent  with  other  known  facts  re- 
lating to  the  same  case;  (3)  it  must  be  consistent  with 
ordinary  experience. 

1.  If  a  witness,  in  one  part  of  his  testimony,  makes 
a  statement  inconsistent  with  what  he  has  stated  pre- 
viously, his  testimony  is  discredited.  One  of  his  state- 
ments may  be  true  or  both  may  be  false;  it  may  be 
possible  to  show  that  one  of  them  is  consistent  with  the 
rest  of  his  testimony,  while  the  other  is  not,  but  the 
disagreement  of  these  statements  would  tend  to  throw 
doubt  upon  the  others,  and  without  external  corrobora- 
tion  his  whole  story  would  be  open  to  question.  More- 
over, his  statements,  to  have  the  greatest  force,  must 
not  only  be  consistent,  they  must  be  coherent ;  they  must 
describe  a  connected  series  of  events.  If  a  lawyer  can 
by  cross-examination  show  that  the  witness  has  made 
inconsistent  statements,  the  force  of  his  testimony  is 
often  entirely  destroyed ;  and  it  is  usually  very  much 
weakened,  at  the  very  least. 

But  even  the  most  coherent  body  of  testimony  would, 
by  itself,  be  insufficient  to  prove  the  existence  of  the 
facts  alleged.  Otherwise  we  should  be  obliged  to  ac- 
cept as  true  many  acknowledged  fictions.  Indeed,  too 
great  coherence,  too  good  a  story,  rouses  the  suspicion 
that  it  has  been  manufactured  or  at  least  modified,  since 
most  men  are  too  inaccurate  both  in  observing  and  in 


276    TYPICAL    SYSTEMS    OF   KNOWLEDGE 

remembering  to  describe  any  complex  set  of  events 
without  minor  inconsistencies. 

By  itself,  then,  internal  evidence  is  not  conclusive; 
without  the  support  of  other  testimony  or  of  facts 
otherwise  known  any  piece  of  testimony  must  be  held 
as  doubtful.  A  possible  exception  might  be  noted: 
if  the  testimony  were  of  such  a  character  that  its  falsity 
would  be  more  difficult  to  understand  and  explain  than 
its  truth,  we  should  have  some  ground  for  accepting 
it  even  in  the  absence  of  other  corroboration ;  but  such 
cases  would  obviously  be  rare. 

Negative  Evidence. — The  absence  of  testimony  to 
the  existence  of  a  fact  which  could  hardly  have  failed 
of  mention  by  contemporaries  is  a  strong  presumption 
against  its  existence.  If  an  alleged  work,  or  doctrine, 
or  what  not,  is  referred  to  by  no  contemporary  and  is 
first  mentioned  by  some  later  writer,  it  is  probably 
false.  The  tradition  regarding  individuals,  cities,  and 
so  on,  often  becomes  more  extensive  and  circumstantial 
as  the  objects  of  the  tradition  get  farther  away.11 

2.  In  oral  testimony,  one  of  the  most  frequent  sources 
of  corroboration  is  to  be  found  in  the  testimony  of 
other  witnesses.  But  too  close  an  agreement,  instead  of 
being  evidence  of  the  truth  of  the  testimony,  raises  a 
suspicion  that  the  witnesses  are  in  collusion  and  that 
the  whole  story  may  be  false.  The  inevitable  inaccu- 
racies of  observation  and  'of  memory  render  it  prac- 
tically impossible  that  two  witnesses  should  tell  stories 
that  should  agree  in  all  particulars ;  some  differences 
are  to  be  expected,  and  sometimes  there  are  differences 
regarding  some  of  the  most  important  points.  In  writ- 

11  For   illustrations,    see    Hay  ward,   Essays,   "The    Pearls    and 
Mock  Pearls  of  History." 


TESTIMONY  277 

ten  testimony,  if  there  are  several  documents  very 
closely  similar,  the  presumption  is  that,  instead  of  being 
independent  pieces  of  testimony,  they  are  all  derived 
from  the  same  source.  This  presumption  is  particu- 
larly strong  if  the  errors  happen  to  be  the  same  in 
all ;  if,  for  example,  the  same  words  are  misspelled  or  the 
same  misstatements  of  fact  are  made  in  all,  this  is 
good  evidence  that  one  of  the  documents  was  the  source 
of  the  rest  or  that  all  were  derived  from  some  common 
source.  Of  course  disagreement  does  not  prove  the 
truth  of  any  one  of  the  bodies  of  testimony,  but  it  is 
good  evidence  of  their  independent  origin.  Where  the 
truth  lies  must  be  discovered  by  further  comparison 
and  construction. 

3.  The  thir.d  test  mentioned  above  was  agreement 
with  ordinary  experience.  What  is  known  as  the  Argu- 
ment to  Antecedent  Probability  would  be  included  here. 
We  ask :  Is  the  alleged  event  one  that  would  have  been 
probable  in  the  circumstances?  Is  it  consistent  with 
the  known  laws  of  nature  and  their  familiar  modes  of 
operation?  This  test  might,  in  practice,  be  applied 
first ;  if,  for  example,  testimony  contained  statements 
violating  all  ordinary  experience  or  well-tested  laws  of 
nature,  we  might  decline  to  go  to  the  trouble  of  ap- 
plying the  other  tests.  But  this  test  is  not  necessarily 
final,  for  statements  which  disagree  with  our  past  ex- 
perience are  very  frequently  found  to  be  true  and  it  has 
more  than  once  happened  that  a  supposed  law  of  na- 
ture has  been  stated  too  broadly  and  has  needed  quali- 
fication. A  too  ready  rejection  of  unusual  statements 
is  no  more  justified  by  a  sound  method  than  is  a  too 
ready  credulity.  But  if  the  application  of  other  tests 
leaves  the  truth  of  the  testimony  inconclusive,  a  viola- 


278    TYPICAL    SYSTEMS    OF    KNOWLEDGE 

tion  of  ordinary  experience  would  warrant  the  rejection 
of  the  testimony.  If  alleged  facts  were  in  contradic- 
tion to  supposed  laws  of  Nature,  their  existence  could 
be  established  only  by  evidence  which  was  stronger  than 
the  whole  body  of  evidence  in  favor  of  the  supposed  law. 
Proof  of  the  violation  of  all  the  laws  of  Nature  would 
be  impossible;  for  all  proof  requires  the  use  of  some 
law.  We  are  often  over-hasty  in  concluding  that  a 
statement  is  inconsistent  with  another  or  with  some  of 
the  consequences  of  the  latter,  and  we  tend  too  readily 
to  condemn  anything  which  is  apparently  inconsistent 
with  established  principles.  Rejection  of  the  Coper- 
nican  Hypothesis  on  the  ground  of  its  inconsistency 
with  the  principles  of  religion  was  a  case  of  this  sort. 

There  are  two  or  three  topics  which  call  for  a  little 
further  discussion  at  this  point.  One  of  these  is  what 
is  known  as  hearsay  evidence;  in  this  the  witness  re- 
ports not  what  he  himself  observed,  but  what  he  has 
heard  some  one  else  describe.  Its  value  is  very  much 
less  than  is  that  of  testimony  to  the  fact  itself.  To  the 
errors  of  the  original  observer,  the  errors  of  observa- 
tion, of  memory,  of  description,  and  possible  bad  faith 
on  the  part  of  the  original  observer,  we  have  added 
those  of  a  second  person,  who  is  liable  to  the  same  errors 
and  defects  with  regard  to  the  words  of  the  first. 

Tradition  is  simply  hearsay  evidence  with  a  multi- 
plication of  the  number  of  intermediates  between  the 
last  hearer  and  the  original  observer,  if  indeed,  there 
were  any  observations  at  the  beginning.  It  is  evident 
that  tradition  is  exceedingly  poor  evidence  of  the  ex- 
istence of  any  fact. 


COMPLETE    SYSTEMS  279 

Circumstantial  evidence  is  merely  indirect  evidence ; 
there  may  be  no  witnesses  who  have  observed  the  facts 
themselves,  but  certain  other  facts  may  be  incapable  of 
explanation  on  any  theory  other  than  the  one  which 
asserts  the  existence  of  these  facts. 

We  have  been  discussing  the  problems  of  discovering 
and  evaluating  historical  facts ;  the  principles  involved 
in  building  up  a  system  when  the  data  are  derived  from 
both  testimony  and  observation  are,  of  course,  the  same 
as  those  involved  in  constructing  a  system  from  data 
obtained  in  any  other  way.  We  wish  to  get  a  complete, 
coherent  whole.  The  framework  of  general  statements 
or  laws,  and  the  particular  structure  which  we  build, 
must  provide  a  place  for  the  facts  which  are  the  ma- 
terials to  be  built  into  a  system.  If  there  are  facts 
which  do  not  fit,  if  there  are  parts  of  the  framework 
which  interfere  with  each  other,  if  the  laws  of  such 
structures  are  violated,  the  construction  can  not  be 
accepted.  A  place  for  every  fact,  and  a  complete  struc- 
ture when  all  the  facts  are  in  place,  are  the  require- 
ments of  a  scientific  structure,  or,  in  other  words,  of 
any  structure  of  knowledge  which  is  to  satisfy  the  de- 
mands of  a  reasonable  being. 

The  details  of  historical  construction  are  beyond  the 
scope  of  this  outline  and  an  illustration  which  should 
show  them  with  any  degree  of  fullness  would  occupy 
too  much  space.  Huxley's  argument,  quoted  on  pages 
287-300),  illustrates  a  few  of  the  points.  The  student 
is  referred  to  Langlois  and  Seignobos's  Introduction  to 
the  Study  of  History  for  further  discussion  and  illus- 
tration. 


280    TYPICAL    SYSTEMS    OF    KNOWLEDGE 


EXERCISES 

In  the  following  examples,  outline  the  argument  and 
state  the  general  principles  employed,  and  the  way  in 
which  these  principles  were  or  might  have  been  estab- 
lished; examine  each  step  in  the  reasoning  and  determine 
whether  or  not  it  is  valid;  where  inductive  inference  is 
used  describe  its  foundation,  and  criticise,  if  possible; 
where  the  argument  is  incomplete  state  'what  would  be 
necessary  in  order  to  complete  it: 

I.  Professor  James's  argument  for  his  theory  of  the 
emotions,  as  given  in  his  Psychology,  Briefer 
Course,  pp.  375  to  380. 

"  The  feeling,  in  the  coarser  emotions,  results  from  the 
bodily  expression.  Our  natural  way  of  thinking  about  the 
coarser  emotions  is  that  the  mental  perception  of  some 
fact  excites  the  mental  affection  called  the  emotion,  and 
that  the  latter  state  of  mind  gives  rise  to  the  bodily  ex- 
pression. My  theory,  on  the  contrary,  is  that  the  bodily 
changes  follow  directly  the  perception  of  the  exciting  fact, 
and  that  our  feeling  of  the  same  changes  as  they  occur  IS 
the  emotion.  Common  sense  says,  we  lose  our  fortune,  are 
sorry  and  weep;  we  meet  a  bear,  are  frightened  and  run; 
we  are  insulted  by  a  rival,  are  angry  and  strike.  The 
hypothesis  here  to  be  defended  says  that  this  order  of 
sequence  is  incorrect,  that  the  one  mental  state  is  not  imme- 
diately induced  by  the  other,  that  the  bodily  manifestations 
must  first  be  interposed  between,  and  that  the  more  rational 
statement  is  that  we  feel  sorry  because  we  cry,  angry  be- 
cause we  strike,  afraid  because  we  tremble,  and  not  that 
we  cry,  strike,  or  tremble  because  we  are  sorry,  angry,  or 
fearful,  as  the  case  may  be.  Without  the  bodily  states 
following  on  the  perception,  the  latter  would  be  purely 
cognitive  in  form,  pale,  colorless,  destitute  of  emotional 
warmth.  We  might  then  see  the  bear  and  judge  it  best  to 
run,  receive  the  insult  and  deem  it  right  to  strike,  but  we 
should  not  feel  afraid  or  angry. 

"  Stated  in  this  crude  way,  the  hypothesis  ir  pretty  sure 


JAMES'   THEORY    OF    EMOTION        281 

to  meet  with  immediate  disbelief.  And  yet  neither  many 
nor  far-fetched  considerations  are  required  to  mitigate  itg 
paradoxical  character,  and  possibly  to  produce  conviction 
of  its  truth. 

"  1.  To  begin  with,  particular  perceptions  certainly  do 
produce  widespread  bodily  effects  by  a  sort  of  immediate 
physical  influence,  antecedent  to  the  arousal  of  an  emotion 
or  emotional  idea.  In  listening  to  poetry,  drama,  or  heroic 
narrative,  we  are  often  surprised  at  the  cutaneous  shiver 
which  like  a  sudden  wave  flows  over  us,  and  at  the  heart- 
swelling  and  lachrymal  effusion  that  unexpectedly  catch 
us  at  intervals.  In  hearing  music  the  same  is  even  more 
strikingly  true.  If  we  abruptly  see  a  dark  moving  form 
in  the  woods,  our  heart  stops  beating,  and  we  catch  our 
breath  instantly  and  before  any  articulate  idea  of  danger 
can  arise.  If  our  friend  goes  near  to  the  edge  of  a  preci- 
pice, we  get  the  well-known  feeling  of  '  all-overishness/ 
and  we  shrink  back,  although  we  positively  know  him  to  be 
safe,  and  have  no  distinct  imagination  of  his  fall.  The 
writer  well  remembers  his  astonishment,  when  a  boy  of 
seven  or  eight,  at  fainting  when  a  horse  was  bled.  The 
blood  was  in  a  bucket,  with  a  stick  in  it,  and,  if  memory 
does  not  deceive  him,  he  stirred  it  round  and  saw  it  drip 
from  the  stick  with  no  feeling  save  that  of  childish  curios- 
ity. Suddenly  the  world  grew  black  before  his  eyes,  his 
ears  began  to  buzz,  and  he  knew  no  more.  He  had  never 
heard  of  the  sight  of  blood  producing  faintness  or  sickness, 
and  he  had  so  little  repugnance  to  it,  and  so  little  appre- 
hension of  any  other  sort  of  danger  from  it,  that  even  at 
that  tender  age,  as  he  well  remembers,  he  could  not  help 
wondering  how  the  mere  physical  presence  of  a  pailful  of 
crimson  fluid  could  occasion  in  him  such  formidable  bodily 
effects. 

"  2.  The  best  proof  that  the  immediate  cause  of  emotion 
is  a  physical  effect  on  the  nerves  is  furnished  by  those 
pathological  cases  in  which  the  emotion  is  objectless.  One 
of  the  chief  merits,  in  fact,  of  the  view  which  I  propose, 
seems  to  be  that  we  can  so  easily  formulate  by  its  means 
pathological  cases  and  normal  cases  under  a  common 
scheme.  In  every  asylum  we  find  examples  of  absolutely 
unmotived  fear,  anger,  melancholy,  or  conceit;  and  others 


TYPICAL    SYSTEMS    OF    KNOWLEDGE 

of  an  equally  unmotived  apathy  which  persists  in  spite  of 
the  best  outward  reasons  why  it  should  give  way.  In  the 
former  cases  we  must  suppose  the  nervous  machinery  to  be 
so  '  labile  '  in  some  one  emotional  direction  that  almost  any 
stimulus  (however  inappropriate)  causes  it  to  upset  in  that 
way,  and  to  engender  the  particular  complex  of  feelings  of 
which  the  psychic  body  of  the  emotion  corresponds.  Thus, 
to  take  one  special  instance,  if  inability  to  draw  a  deep 
breath,  fluttering  of  the  heart,  and  that  peculiar  gastric 
change  felt  as  '  precordial  anxiety/  with  an  irresistible 
tendency  to  take  a  somewhat  crouching  attitude  and  to  sit 
still,  with  perhaps  other  visceral  processes  not  now  known, 
all  spontaneously  occur  together  in  a  certain  person,  his 
feeling  of  the  combination  is  the  emotion  of  dread,  and  he 
is  the  victim  of  what  is  known  as  morbid  fear.  A  friend 
who  has  occasional  attacks  of  this  most  distressing  of  all 
maladies  tells  me  that  in  his  case  the  whole  drama  seems 
to  center  about  the  region  of  the  heart  and  respiratory 
apparatus,  that  his  main  effort  during  the  attacks  is  to  get 
control  of  his  inspirations  and  to  slow  his  heart,  and  that 
the  moment  he  attains  to  breathing  deeply  and  holding  him- 
self erect,  the  dread,  ipso  facto,  seems  to  depart. 

"  The  emotion  here  is  nothing  but  the  feeling  of  a  bodily 
state,  and  it  has  a  purely  bodily  cause. 

"  3.  The  next  thing  to  be  noticed  is  this,  that  every  one 
of  the  bodily  changes,  whatsoever  it  be,  is  FELT,  acutely 
or  obscurely,  the  moment  it  occurs.  If  the  reader  has  never 
paid  attention  to  this  matter  he  will  be  both  interested  and 
astonished  to  learn  how  many  different  bodily  feelings  he 
can  detect  in  himself  as  characteristic  of  his  various  emo- 
tional moods.  It  would  be  perhaps  too  much  to  expect  of 
him  to  arrest  the  tide  of  any  strong  gust  of  passion  for  the 
sake  of  any  such  curious  analysis  as  this ;  but  he  can  observe 
more  tranquil  states,  and  that  may  be  assumed  to  be  true 
of  the  greatest  which  is  shown  to  be  true  of  the  less.  Our 
whole  cubic  capacity  is  sensibly  alive;  and  each  morsel  of 
it  contributes  its  pulsations  of  feeling,  dim  or  sharp, 
pleasant,  painful,  or  dubious,  to  that  sense  of  personality 
that  every  one  of  us  unfailingly  carries  with  him.  It  is 
surprising  what  little  items  give  accent  to  these  complexes 
of  sensibility.  When  worried  by  any  slight  trouble,  one 


JAMES'    THEORY    OF    EMOTION        283 

may  find  that  the  focus  of  one's  bodily  consciousness  is  the 
contraction,  often  quite  inconsiderable,  of  the  eyes  and: 
brows.  When  momentarily  embarrassed,  it  is  something  in 
the  pharynx  that  compels  either  a  swallowing,  a  clearing 
of  the  throat,  or  a  slight  cough;  and  so  on  for  as  many 
more  instances  as  might  be  named.  The  various  permuta- 
tions of  which  these  organic  changes  are  susceptible  make 
it  abstractly  possible  that  no  shade  of  emotion  should  be 
without  a  bodily  reverberation  as  unique,  when  taken  in  its 
totality,  as  is  the  mental  mood  itself.  The  immense  num- 
ber of  parts  modified  is  what  makes  it  so  difficult  for  us  to 
reproduce  in  cold  blood  the  total  and  integral  expression  of 
any  one  emotion.  We  may  catch  the  trick  with  the  vol- 
untary muscles,  but  fail  with  the  skin,  glands,  heart,  and 
other  viscera.  Just  as  an  artificially  imitated  sneeze  lacks 
something  of  the  reality,  so  the  attempt  to  imitate  grief 
or  enthusiasm  in  the  absence  of  its  normal  instigating  cause 
is  apt  to  be  rather  '  hollow.' 

"  4.  I  now  proceed  to  the  vital  point  of  my  whole  theory, 
which  is  this:  If  we  fancy  some  strong  emotion,  and  then 
try  to  abstract  from  our  consciousness  of  it  all  the  feelings 
of  its  bodily  symptoms,  we  find  we  have  nothing  left  behind, 
no  '  mind  stuff '  out  of  which  the  emotion  can  be  con- 
stituted, and  that  a  cold  and  neutral  state  of  intellectual 
perception  is  all  that  remains.  It  is  true  that,  although 
most  people,  when  asked,  say  that  their  introspection  verifies 
tfiis  statement,  some  persist  in  saying  that  theirs  does  not. 
Many  of  them  cannot  be  made  to  understand  the  question. 
When  you  beg  them  to  imagine  away  every  feeling  of  laugh- 
ter and  of  the  tendency  to  laugh  from  their  conscious- 
ness of  the  ludicrousness  of  the  object,  and  then  to  tell 
you  what  the  feeling  of  its  ludicrousness  is  like,  whether 
it  be  anything  more  than  the  perception  that  the  object 
belongs  to  the  class  '  funny,'  they  persist  in  replying  that 
the  thing  is  a  physical  impossibility,  and  they  always  must 
laugh  if  they  see  a  funny  object.  Of  course  the  task  pro- 
posed is  not  the  impossible  one  of  seeing  a  ludicrous  object 
and  annihilating  one's  tendency  to  laugh.  It  is  the  purely 
speculative  one  of  subtracting  certain  elements  of  feeling 
from  an  emotional  state  supposed  to  exist  in  its  fullness, 
and  saying  what  the  residual  elements  are.  I  cannot  help 


284    TYPICAL    SYSTEMS    OF    KNOWLEDGE 

thinking  that  all  who  rightly  apprehend  this  problem  will 
agree  with  the  proposition  above  laid  down.  What  kind  of 
an  emotion  of  fear  would  be  left  if  the  feeling  neither  of 
quickened  heart-beats  nor  of  shallow  breathing,  neither 
of  trembling  lips  nor  of  weakened  limbs,  neither  of  goose- 
flesh  nor  of  visceral  stirrings,  were  present,  it  is  quite  im- 
possible for  me  to  think.  Can  one  fancy  the  state  of  rage 
and  picture  no  ebullition  in  the  chest,  no  flushing  of  the 
face,  no  dilatation  of  the  nostrils,  no  clenching  of  the  teeth, 
no  impulse  to  vigorous  action,  but  in  their  stead  limp  mus- 
cles, calm  breathing,  and  a  placid  face?  The  present 
writer,  for  one,  certainly  cannot.  The  rage  is  as  com- 
pletely evaporated  as  the  sensation  of  its  so-called  mani- 
festations, and  the  only  thing  that  can  possibly  be  sup- 
posed to  take  its  place  is  some  cold-blooded  and  dispas- 
sionate judicial  sentence,  confined  entirely  to  the  intellec- 
tual realm,  to  the  effect  that  a  certain  person  or  persons 
merit  chastisement  for  their  sins.  In  like  manner  of  grief: 
what  would  it  be  without  its  tears,  its  sobs,  its  suffocation 
of  the  heart,  its  pang  in  the  breast  bone?  A  feelingless 
cognition  that  certain  circumstances  are  deplorable  and 
nothing  more.  Every  passion  in  turn  tells  the  same  story. 
A  disembodied  human  emotion  is  a  sheer  nonentity.  I  do 
not  say  that  it  is  a  contradiction  in  the  nature  of  things, 
or  that  pure  spirits  are  necessarily  condemned  to  cold, 
intellectual  lives ;  but  I  say  that  for  us  emotion  disassociated 
from  all  bodily  feeling  is  inconceivable.  The  more  closely 
I  scrutinize  my  states,  the  more  persuaded  I  become  that 
whatever  '  coarse '  affections  and  passions  I  have  are  in 
very  truth  constituted  by,  and  made  up  of,  those  bodily 
changes  which  we  ordinarily  call  their  expression  or  con- 
sequence; and  the  more  it  seems  to  me  that,  if  I  were  to 
become  corporeally  anaesthetic,  I  should  be  excluded  from 
the  life  of  the  affections,  harsh  and  tender  alike,  and  drag 
out  an  existence  of  merely  cognitive  or  intellectual  form." 

II.  Extract  from  a  lecture  by  A.  H.  Fison  on  "  The 
Evolution  of  Double  Stars  "  in  Lectures  on  the 
Method  of  Science,  Edited  by  T.  B.  Strong: 

The  leading  points  of  Darwin's  12  investigations  of  the 
12  Professor  George  Darwin. 


DOUBLE    STARS  285 

past  history  of  the  moon:  "  From  the  fact  that  the  intensity 
of  the  moon's  attraction  is  greater  upon  the  parts  of  the 
Earth  that  are  nearer  to  it  than  upon  the  parts  that  are 
more  remote  there  arises  a  tendency  for  the  earth  to  be- 
come stretched  along  the  diameter  that  is  at  that  particular 
instant  directed  towards  the  Moon.  If  the  Earth  were 
fluid,  it  would  yield  to  this  tendency,  but,  as  it  is  in  the 
main  solid,  it  is  unable  to  do  so.  The  waters  upon  its 
surface  are,  however,  free,  and  they  consequently  flow,  con- 
tinually tending  to  accumulate  in  two  high  tides,  one  im- 
mediately under  the  Moon,  and  the  other  at  the  part  of  the 
Earth's  surface  that  is  most  remote  from  it.  If  the  period 
of  the  Earth's  rotation  was  the  same  as  that  of  the  Moon's 
revolution  round  it,  the  Moon  would  continually  face  the 
same  regions  of  the  Earth,  and  in  the  course  of  time,  pos- 
sibly a  few  months  or  years,  the  water  would  reach  a 
position  of  equilibrium,  forming  permanent  high  tides  at 
the  opposite  ends  of  the  diameter  that  would  then  be  per- 
manently directed  to  the  Moon. 

"  This  simple  condition  is,  however,  profoundly  modified 
by  the  Earth's  rotation.  As  the  Earth  turns  under  the 
Moon  in  a  period  of  slightly  less  than  twenty-five  hours, 
the  regions  presented  to  the  Moon — those  at  which  the 
water  tends  to  accumulate — are  continually  changing,  and 
before  any  portion  of  water  could  move  appreciably  to- 
wards them,  the  forces  acting  upon  it  would  change  it  and 
it  would  be  urged  in  some  other  direction.  The  problem 
thus  becomes  extremely  complicated.  The  general  result, 
however,  is,  that  in  its  continual  endeavor  to  move  towards 
the  ends  of  the  terrestrial  diameter  that  is  at  each  given 
instant  pointing  to  the  Moon,  the  water  on  the  Earth's 
surface  is  thrown  into  the  continual  motion  that  we  recog- 
nize as  tidal  ebb  and  flow. 

"If  the  movement  of  the  water  were  urrresisted  by  fric- 
tion, tidal  ebb  and  flow  would  possess  no  cosmical  signifi- 
cance, but  friction  is  experienced  in  the  motion  of  the  tidal 
wave  over  the  surface  of  shores  and  estuaries,  and  in  in- 
ternal motions  of  the  water  itself.  The  destruction  of 
motion  by  friction  develops  heat,  and  the  Earth  is  conse- 
quently warmed  by  its  tides;  moreover,  since  heat  is  a 
form  of  energy,  some  other  form  of  energy,  equivalent  in 


TYPICAL    SYSTEMS    OF    KNOWLEDGE 

amount,  must  disappear  in  producing  it.  From  considera- 
tions of  a  not  very  difficult  nature,  it  can  be  shown  that  this 
energy  is  that  of  the  Earth's  rotation,  so  that  we  are  pre- 
sented with  the  remarkable  fact  that  the  speed  of  the 
Earth's  rotation  is  being  reduced  in  consequence  of  the 
tides.  The  period  of  the  Earth's  rotation  determines  the 
day,  and  consequently  the  day  must  be  increasing  in  length. 
No  doubt  the  rate  of  increase  is  now  very  slight,  but  there 
can  be  little  doubt  that  this  has  not  always  been  the  case. 
The  Earth  was  at  one  time  a  mass  of  molten  rock,  in  which 
bodily  tides  must  have  been  formed,  while  friction  must 
have  been  far  greater  in  the  case  of  such  a  viscous  mass 
than  in  water.  Further,  as  we  shall  see,  the  Moon  must 
have  been  nearer  the  Earth  than  it  is  now,  and  its  tide- 
producing  power  consequently  more  intense.  Under  these 
conditions  we  can  well  imagine  that  the  loss  of  rotation 
proceeded  at  a  comparatively  rapid  pace,  and  that  the  day 
was  formerly  far  shorter  than  it  is  at  the  present  time. 

"  The  slackening  of  the  Earth's  rotation  is  not,  however, 
the  only  result  of  tidal  friction.  A  reaction  upon  the  Moon 
is  inevitable,  and  it  appears  that,  as  a  necessary  conse- 
quence, the  Moon  must  recede  from  the  Earth,  its  orbital 
speed  decreasing  at  the  same  time.  Its  period  of  revolu- 
tion round  the  Earth,  which  we  may  define  as  the  month, 
is  therefore  increasing,  so  that  in  consequence  of  the  tides, 
the  day  and  the  month  are  both  becoming  longer.  It  fol- 
lows, however,  from  simple  considerations,  that  this  cannot 
continue  indefinitely.  The  day  is  increasing,  and  so  also 
is  the  month,  but  there  must  come  a  time  when  the  day  must 
increase  more  rapidly  than  the  month  (already  past),  and 
it  must  ultimately  overtake  it.  The  length  of  each  will 
then  be  fifty-five  of  our  present  days.  The  Earth,  then 
rotating  in  the  same  period  as  that  of  the  Moon's  revolution 
round  it,  will  continually  present  the  same  regions  to  the 
Moon,  as  the  Moon  already  presents  the  same  face  to  it. 
At  the  ends  of  the  terrestrial  diameter  that  will  then  be 
constantly  pointing  towards  the  Moon,  permanent  high 
tides  will  accumulate;  ebb  and  flow,  and  with  it  tidal  fric- 
tion will  cease,  and  a  state  of  stable  equilibrium  will  be 
reached.  It  is  impossible  to  determine  the  epoch  of  this 
stage,  but  under  the  most  favorable  conditions  it  must  be 


DOUBLE    STARS  287 

measured  by  hundreds  of  millions  of  years  from  the  present 
time.  ...  In  the  past  the  Earth  must  have  rotated 
more  rapidly,  the  Moon  must  have  been  nearer,  and  it  must 
have  revolved  in  a  shorter  period  than  at  present.  From 
the  application  of  mathematics  to  the  problem,  Darwin  has 
shown  that  there  must  have  been  a  time  when  the  Moon 
was  quite  close  to  the  surface  of  the  Earth,  and,  when  in 
this  condition,  the  further  suggestive  fact  appears  that  its 
period  of  revolution,  the  month,  coincided,  as  it  will  again 
coincide  in  the  last  stage,  with  that  of  the  Earth's  rotation, 
the  day.  Both  must  then  have  been  between  three  and 
five  hours  in  length.  In  this  first,  as  in  the  last  condition, 
we  see  Earth  and  Moon  rotating  as  a  whole  about  their 
common  center  of  mass,  each  continually  presenting  the 
same  face  to  each  other.  While,  however,  in  the  first  con- 
dition they  are  nearly  in  contact  and  represent  a  passing 
phase,  in  the  last  they  are  far  apart,  and  their  condition 
is  permanent.  It  is  possible  to  show  that  the  first  stage 
could  not  have  occurred  less  than  50,000,000  years  ago." 


III.  Huxley's  lecture  on  "  The  Demonstrative  Evidence 
of  Evolution  "   (with  a  few  omissions)  : 

"  The  occurrence  of  historical  facts  is  said  to  be  demon- 
strated, when  the  evidence  that  they  happened  is  of  such 
a  character  as  to  render  the  assumption  that  they  did  not 
happen  in  the  highest  degree  improbable;  and  the  question 
I  now  have  to  deal  with  is,  whether  evidence  in  favor  of 
the  evolution  of  animals  of  this  degree  of  cogency  is,  or  is 
not,  obtainable  from  the  record  of  the  succession  of  living 
forms  which  is  presented  to  us  by  fossil  remains. 

"  Those  who  have  attended  to  the  progress  of  palaeon- 
tology are  aware  that  evidence  of  the  character  which  I 
have  defined  has  been  produced  in  considerable  and  con- 
tinually increasing  quantity  during  the  last  few  years.  In- 
deed, the  amount  and  the  satisfactory  nature  of  that 
evidence  are  somewhat  surprising,  when  we  consider  the 
conditions  under  which  alone  we  can*  hope  to  obtain  it. 

"  It  is  obviously  useless  to  seek  for  such  evidence,  except 
in  localities  in  which  the  physical  conditions  have  been 


288    TYPICAL    SYSTEMS    OF    KNOWLEDGE 

such  as  to  permit  of  the  deposit  of  an  unbroken,  or  but 
rarely  interrupted,,  series  of  strata  through  a  long  period 
of  time;  in  which  the  group  of  animals  to  be  investigated 
has  existed  in  such  abundance  as  to  furnish  the  requisite 
supply  of  remains;  and  in  which,  finally,  the  materials 
composing  the  strata  are  such  as  to  insure  the  preservation 
of  these  remains  in  a  tolerably  perfect  and  undisturbed 
state. 

"  It  so  happens  that  the  case  which,  at  present,  most 
nearly  fulfills  all  these  conditions  is  that  of  the  series  of 
extinct  animals  which  culminates  in  the  Horses;  by  which 
term  I  mean  to  denote  not  merely  the  domestic  animals 
with  which  we  are  so  well  acquainted,  but  their  allies,  the 
ass,  zebra,  quagga,  and  the  like.  In  short,  I  use  '  horses  ' 
as  the  equivalent  of  the  technical  term  Equidce,  which  is 
applied  to  the  whole  group  of  existing  equine  animals. 

"  The  horse  is  in  many  ways  a  remarkable  animal;  not 
least  so  in  the  fact  that  it  presents  us  with  air  example  of 
one  of  the  most  perfect  pieces  of  machinery  in  the  living 
world.  In  truth,  among  the  works  of  human  ingenuity  it 
cannot  be  said  that  there  is  any  locomotive  so  perfectly 
adapted  to  its  purposes,  doing  so  much  work  with  so  small 
a  quantity  of  fuel,  as  this  machine  of  nature's  manufacture 
— the  horse.  .  ^  .  .  Look  at  the  perfect  balance  of  his 
form,  and  the  rhythm  and  force  of  its  action.  The  loco- 
motive machinery  is,  as  you  are  aware,  resident  in  its 
slender  fore  and  hind  limbs;  they  are  flexible  and  elastic 
levers,  capable  of  being  moved  by  very  powerful  muscles; 
and,  in  order  to  supply  the  engines  which  work  these  levers 
with  the  force  which  they  expend,  the  horse  is  provided  with 
a  very  perfect  apparatus  for  grinding  its  food  and  extract- 
ing therefrom  the  requisite  fuel. 

"  Without  attempting  to  take  you  very  far  into  the 
region  of  osteological  detail,  I  must  nevertheless  trouble 
you  with  some  statements  respecting  the  anatomical  struc- 
ture of  the  horse;  and,  more  especially,  will  it  be  needful 
to  obtain  a  general  conception  of  the  structure  of  its  fore 
and  hind  limbs,  and  of  its  teeth.  But  I  shall  only  touch 
upon  those  points  which  are  absolutely  essential  to  our 
inquiry. 

"  Let  us  turn   in  the  first  place  to  the  fore-limb.     In 


HUXLEY    ON    EVOLUTION  289 

most  quadrupeds,  as  in  ourselves,  the  fore-arm  contains 
distinct  bones,  called  the  radius  and  the  ulna.  The  cor- 
responding region  in  the  horse  seems  at  first  to  possess  but 
one  bone.  Careful  observation,  however,  enables  us  to 
distinguish  in  this  bone  a  part  which  clearly  answers  to  the 
upper  eird  of  the  ulna.  This  is  closely  united  with  the  chief 
mass  of  the  bone  which  represents  the  radius,  and  runs 
out  into  a  slender  shaft  which  may  be  traced  for  some  dis- 
tance downwards  upon  the  back  of  the  radius,  and  then  in 
most  cases  thins  out  and  vanishes.  It  takes  still  more 
trouble  to  make  sure  of  what  is  nevertheless  the  fact,  that 
a  small  part  of  the  lower  end  of  the  bone  of  a  horse's  fore- 
arm, which  is  only  distinct  in  a  very  young  foal,  is  really 
the  lower  extremity  of  the  ulna. 

"  What  is  commonly  called  the  knee  of  a  horse  is  its 
wrist.  The  '  cannon  bone '  answers  to  the  middle  bone 
of  the  five  metacarpal  bones,  which  support  the  palm  of 
the  hand  in  ourselves.  The  '  pastern/  '  coronary/  and 
'  coffin'  bones  of  veterinarians  answer  to  the  joints  of  our 
middle  fingers,  while  the  hoof  is  simply  a  greatly  enlarged 
and  thickened  nail.  But  if  what  lies  below  the  horse's 
'  knee '  thus  corresponds  to  the.  middle  finger  in  ourselves, 
what  has  become  of  the  four  other  fingers  or  digits?  We 
find  in  the  places  of  the  second  and  fourth  digits  only  two 
slender,  splint-like  bones,  about  two-thirds  as  long  as  the 
cannon  bone,  which  gradually  taper  to  the  lower  ends  and 
bear  no  finger  joints,  or  as  they  are  termed,  phalanges. 
Sometimes,  small  bony  or  gristly  nodules  are  to  be  found 
at  the  bases  of  these  two  metacarpal  splints,  and  it  is  prob- 
able that  these  represent  rudiments  of  the  first  and  fifth 
toes.  Thus  the  part  of  the  horse's  skeleton  which  cor- 
responds with  that  of  the  human  hand  contains  one  over- 
grown middle  digit,  and  at  least  two  imperfect  lateral 
digits;  and  these  answer,  respectively,  to  the  third,  the 
second,  and  the  fourth  fingers  in  man. 

"  Corresponding  modifications  are  found  in  the  hind 
limb.  In  ourselves,  and  in  most  quadrupeds,  the  leg  con- 
tains two  distinct  bones — a  large  bone,  the  tibia,  and  a 
smaller  and  more  slender  bone,  the  fibular.  But,  in  the 
horse,  the  fibular  seems,  at  first,  to  be  reduced  to  its  upper 
end ;  a  short,  slender  bone,  united  with  the  tibia  and  ending 


290    TYPICAL    SYSTEMS    OF    KNOWLEDGE 

in  a  point  below,  occupying  its  place.  Examination  of  the 
lower  end  of  a  young  foal's  shin-bone,  however,  shows  a 
distinct  portion  of  osseous  matter  which  is  the  lower  end  of 
the  fibula;  so  that  the  apparently  single  lower  end  of  the 
shin-bone  is  really  made  up  of  the  coalesced  ends  of  the 
tibia  and  fibula,  just  as  the  apparently  single  lower  end 
of  the  fore-arm  bone  is  composed  of  the  coalesced  radius 
and  ulna. 

"  The  heel  of  the  horse  is  the  part  commonly  known  as 
the  hock.  The  hinder  cannon  bone  answers  to  the  middle 
metatarsal  bone  of  the  human  foot;  the  pastern,  coronary, 
and  coffin  bones,  to  the  middle  toe  bones;  the  hind  hoof  to 
the  nail;  as  in  the  fore-foot.  And,  as  in  the  fore- foot, 
there  are  merely  two  splints  to  represent  the  second  and 
the  fourth  toes.  Sometimes  a  rudiment  of  the  fifth  toe 
appears  to  be  traceable. 

"  The  teeth  of  the  horse  are  not  less  peculiar  than  its 
limbs.  The  living  engine,  like  all  others,  must  be  well  stoked 
if  it  is  to  do  its  work;  and  the  horse,  if  it  is  to  make 
good  its  wear  and  tear,  and  to  exert  the  enormous  amount 
of  force  required  for  its  propulsion,  must  be  well  and 
rapidly  fed.  To  this  end>  good  cutting  instruments  and 
powerful  and  lasting  crushers  are  needful.  Accordingly, 
the  twelve  cutting  teeth  of  a  horse  are  close-set  and  con- 
centrated in  the  fore  part  of  its  mouth,  like  so  many  adzes 
or  chisels.  The  grinders  or  molars  are  large,  and  have 
an  extremely  complicated  structure,  being  composed  of  a 
number  of  different  substances  of  unequal  hardness.  The 
consequence  of  this  is  that  they  wear  away  at  different 
rates;  and,  hence,  the  surface  of  each  grinder  is  always  as 
uneven  as  that  of  a  good  mill-stone. 

"  I  have  said  that  the  structure  of  the  grinding  teeth  is 
very  complicated,  the  harder  and  the  softer  parts  being, 
as  it  were,  interlaced  with  one  another.  The  result  of  this 
is  that,  as  the  tooth  wears,  the  crown  presents  a  peculiar 
pattern,  the  nature  of  which  is  not  very  easily  deciphered  at 
first,  but  which  it  is  important  that  we  should  understand 
clearly.  Each  grinding  tooth  of  the  upper  jaw  has  an 
outer  wall  so  shaped  that,  on  the  worn  crown,  it  exhibits 
the  form  of  two  crescents,  one  in  front  and  one  behind, 
with  their  concave  sides  turned  outwards.  From  the  inner 


HUXLEY    ON   EVOLUTION  291 

sides  of  the  front  crescent,  a  crescentic  front  ridge  passes 
inwards  and  backwards,  and  its  inner  face  enlarges  into  a 
strong  logitudinal  fold  or  pillar.  From  the  front  part  of 
the  hinder  crescent,  a  back-ridge  takes  a  like-  direction,  and 
also  has  its  pillar. 

"  The  deep  interspaces  or  valleys  between  these  ridges 
and  the  outer  wall  are  filled  by  bony  substance,  which  is 
called  cement,  and  coats  the  whole  tooth. 

"  The  pattern  of  the  worn  face  of  each  grinding  tooth  of 
the  lower  jaw  is  quite  different.  It  appears  to  be  formed 
of  two  crescent-shaped  ridges,  the  convexities  of  which  are 
turned  outwards.  The  free  extremity  of  each  crescent  has 
a  pillar,  and  there  is  a  large  double  pillar  where  the  two 
crescents  meet.  The  whole  structure  is,  as  it  were,  em- 
bedded in  cement,  which  fills  up  the  valleys,  as  in  the 
upper  grinders. 

"If  the  grinding  faces  of  an  upper  and  of  a  lower 
molar  are  applied  together,  it  will  be  seen  that  the  opposed 
ridges  are  nowhere  parallel,  but  that  they  frequently  cross ; 
and  that  thus,  in  the  act  of  mastication,  a  hard  surface 
in  the  one  is  constantly  applied  to  a  soft  surface  in  the 
other  and  vice  versa.  They  thus  constitute  a  grinding  ap- 
paratus of  great  efficiency,  and  one  which  is  repaired  as  fast 
as  it  wears,  owing  to  the  long  continued  growth  of  the 
teeth. 

"  Some  other  peculiarities  of  the  dentition  of  the  horse 
must  be  noticed,  as  they  bear  upon  what  I  shall  have  to 
say  by-and-by.  Thus,  the  crowns  of  the  cutting  teeth 
have  a  peculiar  deep  pit,  which  gives  rise  to  the  well-known 
'  mark '  of  the  horse.  There  is  a  large  space  between  the 
outer  incisors  and  the  front  grinder.  In  this  space  the 
adult  male  horse  presents,  near  the  incisors,  one  on  each 
side,  above  and  below,  a  canine  or  '  tush,'  which  is  com- 
monly absent  in  mares.  In  a  young  horse,  moreover,  there 
is  not  infrequently  to  be  seen,  in  front  of  the  first  grinder, 
a  very  small  tooth,  which  soon  falls  out.  If  this  small  tooth 
be  counted  as  one,  it  will  be  found  that  there  are  seven 
teeth  behind  the  canine  on  each  side,  namely,  the  small 
tooth  in  question,  and  six  great  grinders,  among  which,  by 
an  unusual  peculiarity,  the  foremost  tooth  is  rather  larger 
than  those  which  follow  it. 


292    TYPICAL    SYSTEMS    OF    KNOWLEDGE 

"  I  have  now  enumerated  those  characteristic  structures 
of  the  horse  which  are  of  most  importance  for  the  pur- 
pose we  have  in  view. 

"  To  any  one  who  is  acquainted  with  the  morphology  of 
vertebrated  animals,  they  show  that  the  horse  deviates 
widely  from  the  general  structure  of  mammals;  and  that 
the  horse  type  is,  in  many  respects,  an  extreme  modifica- 
tion of  the  general  mammalian  plan.  The  least  modified 
mammals,  in  fact,  have  the  radius  and  ulna,  the  tibia  and 
fibula,  distinct  and  separate.  They  have  five  distinct  and 
complete  digits  on  each  foot,  and  no  one  of  these  digits 
is  very  much  larger  than  the  rest.  Moreover,  in  the  least 
modified  mammals,  the  total  number  of  the  teeth  is  very 
generally  forty-four,  while  in  horses  the  usual  number  is 
forty,  and  in  the  absence  of  the  canines  it  may  be  reduced 
to  thirty-six;  the  incisor  teeth  are  devoid  of  the  fold  seen 
in  those  of  the  horse;  the  grinders  regularly  diminish  in 
size  from  the  middle  of  the  series  to  its  front  end;  while 
their  crowns  are  short,  early  attain  their  full  length,  and 
exhibit  simple  ridges  or  tubercles,  in  place  of  the  complex 
foldings  of  the  horse's  grinders. 

"  Hence,  the  general  principles  of  the  hypothesis  of  evo- 
lution lead  to  the  conclusion  that  the  horse  must  have  been 
derived  from  some  quadruped  which  possessed  five  com- 
plete digits  on  each  foot;  which  had  the  bones  of  the  fore- 
arm and  of  the  leg  complete  and  separate;  and  which 
possessed  forty-four  teeth,  among  which  the  crowns  of  the 
incisors  and  grinders  had  a  simple  structure,  while  the  lat- 
ter gradually  increased  in  size  from  before  backwards,  at 
any  rate  in  the  anterior  part  of  the  series,  and  had  short 
crowns. 

"  And  if  the  horse  has  been  thus  evolved,  and  the  remains 
of  the  different  stages  of  its  evolution  have  been  preserved, 
they  ought  to  present  us  with  a  series  of  forms  in  which  the 
number  of  the  digits  becomes  reduced;  the  bones  of  the 
fore-arm  and  leg  gradually  take  on  the  equine  condition*; 
and  the  form  and  arrangement  of  the  teeth  successively 
approximate  to  those  which  obtain  in  existing  horses. 

"  Let  us  turn  to  the  facts  and  see  how  far  they  fulfil 
these  requirements  of  the  doctrine  of  evolution. 

"  In  Europe  abundant  remains  of  horses  are  found  in 


HUXLEY    ON    EVOLUTION  293 

the  Quaternary  and  later  Tertiary  strata  as  far  as  the 
Pliocene  formation.  But  these  horses,  which  are  so  com- 
mon in  the  cave  deposits  and  in  the  gravels  of  Europe, 
are  in  all  essential  respects  like  existing  horses.  And  that 
is  true  of  all  the  horses  of  the  latter  part  of  the  Pliocene 
epoch.  But  in  deposits  which  belong  to  the  earlier  Plio- 
cene and  later  Miocene  epochs,  and  which  occur  in  Britain, 
in  France,  in  Germany,  in  Greece,  in  India,  we  find  ani- 
mals which  are  extremely  like  horses — which,  in  fact,  are 
so  similar  to  horses,  that  you  may  follow  descriptions  given 
in  works  upon  the  anatomy  of  the  horse  upon  the  skeletons 
of  these  animals — but  which  differ  in  some  important  par- 
ticulars. For  example,  the  structure  of  their  fore  and  hind 
limbs  is  somewhat  different.  The  bones  which,  in  the 
horse,  are  represented  by  two  splints,  imperfect  below,  are 
as  long  as  the  metacarpal  and  metatarsal  bones;  and  at- 
tached to  the  extremity  of  each  is  a  digit  with  three  joints 
of  the  same  general  character  as  those  of  the  middle  digit, 
only  very  much  smaller.  These  small  digits  are  so  disposed 
that  they  could  have  had  but  very  little  functional  impor- 
tance, and  they  must  have  been  rather  of  the  nature  of 
the  dew-claws,  such  as  are  to  be  found  in  many  animals. 
The  Hipparion,  as  the  extinct  European  three-toed  horse 
is  called,  in  fact,  presents  a  foot  similar  to  that  of  the 
American  Protophippus  (Fig.  12),  except  that,  in  the  Hip- 
parion, the  smaller  digits  are  situated  further  back,  and 
are  of  smaller  proportional  size,  than  in  the  Protohippus. 

"  The  ulna  is  slightly  more  distinct  than  in  the  horse ; 
and  the  whole  length  of  it,  as  a  very  slender  shaft,  inti- 
mately united  with  the  radius,  is  completely  traceable.  The 
fibula  appears  to  be  in  the  same  condition  as  in  the  horse. 
The  teeth  of  the  Hipparion  are  essentially  similar  to  those 
of  the  horse,  but  the  pattern  of  the  grinders  is  in  some 
respects  a  little  more  complex,  and  there  is  a  depression 
on  the  face  of  the  skull  in  front  of  the  orbit  which  is  not 
seen  in  existing  horses. 

"  In  the  earlier  Miocene  and  perhaps  the  later  Eocene 
deposits  of  some  parts  of  Europe,  another  extinct  animal 
has  been  discovered,  which  Cuvier,  who  first  described 
some  fragments  of  it,  considered  to  be  a  Palceotherium. 
But  as  further  discoveries  threw  no  light  upon  its  struc- 


294    TYPICAL    SYSTEMS    OF    KNOWLEDGE 

ture,  it  was  recognized  as  a  distinct  genus,  under  the  name 
of  Anchitherium. 

"  In  its  general  characters,  the  skeleton  of  Anchitherium 
is  very  similar  to  that  of  the  horse.  In  fact,  Lartet  and 
De  Blainville  called  it  Palceotherium  equinum  or  hippoides; 
and  De  Christol,  in  1847,  said  that  it  differed  from  Hip- 
parion  in  little  more  than  the  characters  of  its  teeth,  and 
gave  it  the  name  of  Hipparitherium.  Each  foot  possesses 
three  complete  toes;  while  the  lateral  toes  are  much  larger 
in  proportion  to  the  middle  toe  than  in  Hipparwn,  and 
doubtless  rested  on  the  ground  in  ordinary  locomotion. 

"  The  ulna  is  complete  and  quite  distinct  from  the 
radius,  though  firmly  united  with  the  latter.  The  fibula 
seems  also  to  have  been  complete.  Its  lower  end,  though 
intimately  united  with  that  of  the  tibia,  is  clearly  marked 
off  from  the  latter  bone. 

"  There  are  forty-four  teeth.  The  incisors  have  no 
Strong  pit.  The  canines  seem  to  be  well  developed  in  both 
:  sexes.  The  first  of  the  seven  grinders,  which,  as  I  have 
;said,  is  frequently  absent,  and,  when  it  does  exist,  is  small 
in  the  horse,  is  a  good-sized  and  permanent  tooth,  while 
tthe  grinder  which  follows  it  is  but  little  larger  than  the 
ihinder  one.  The  crowns  of  the  grinders  are  short,  and 
though  the  fundamental  pattern  of  the  horse-tooth  is  dis- 
cernible, the  front  and  back  ridges  are  less  curved,  the 
accessory  pillars  are  wanting,  and  the  valleys,  much  shal- 
lower, are  not  filled  up  with  cement. 

"  Seven  years  ago,  when  I  happened  to  be  looking  criti- 
cally into  the  bearing  of  palaeorrtological  facts  upon  the 
(doctrine  of  evolution,  it  appeared  to  me  that  the  Anchithe- 
Tium,  the  Hipparion,  and  the  modern  horse  constitute  a 
series  in  which  the  modifications  of  structure  coincide  with 
the  order  of  chronological  occurrence,  in  the  manner  in 
which  they  must  coincide  if  the  modern  horses  really  are 
the  result  of  a  gradual  metamorphosis,  in  the  course  of  the 
Tertiary  epoch,  of  a  less  specialized  ancestral  form.  And 
I  found  by  correspondence  with  the  late  eminent  French 
anatomist  and  paleontologist,  M.  Lartet,  that  he  had  arrived 
at  the  same  conclusion  from  the  same  data. 

"  That  the  Anchitherium  type  had  become  metamor- 
phosed into  the  Hipparion  type,  and  the  latter  into  the 
Equine  type,  in  the  course  of  that  period  of  time  which 


HUXLEY    ON    EVOLUTION  295 

is  represented  by  the  latter  half  of  the  Tertiary  deposits, 
seemed  to  me  to  be  the  only  explanation  of  the  facts  for 
which  there  was  even  a  shadow  of  probability. 

"  And,  hence,  I  have  ever  since  held  that  these  facts 
afford  evidence  of  the  occurrence  of  evolution,  which,  in 
the  sense  already  defined,  may  be  termed  demonstrative. 

"  All  who  have  occupied  themselves  with  the  structure 
of  Anchitherium,  from  Cuvier  onwards,  have  acknowledged 
its  many  points  of  likeness  to  a  well-known  genus  of  ex- 
tinct Eocene  mammals,  P  alee  other  mm.  Indeed,  as  we  have 
seen,  Cuvier  regarded  his  remains  of  Anchitherium  as  those 
of  a  species  of  Palceotherium.  Hence,  in  attempting  to 
trace  the  pedigree  of  the  horse  beyond  the  Miocene  epoch 
and  the  Anchitheroid  form,  I  naturally  sought  among  the 
various  species  of  Palseotheroid  animals  for  its  nearest 
ally,  and  I  was  led  to  conclude  that  the  Palceotherium  minus 
(Plagiolophus)  represented  the  next  step  more  nearly  than 
any  other  form  then  known. 

"  I  think  that  this  opinion  was  fully  justifiable;  but  the 
progress  of  investigation  has  thrown  an  unexpected  light 
on  the  question,  and  has  brought  us  much  nearer  than  could 
have  been  anticipated  to  a  knowledge  of  the  true  series  of 
the  progenitors  of  the  horse. 

"  You  are  all  aware  that  when  your  country  was  first 
discovered  by  Europeans,  there  were  no  traces  of  the  ex- 
istence of  the  horse  in  any  part  of  the  American  continent. 
The  accounts  of  the  conquest  of  Mexico  dwell  upon  the 
astonishment  of  the  natives  of  that  country  when  they  first 
became  acquainted  with  that  astounding  phenomenon — a 
man  seated  upon  a  horse.  Nevertheless,  the  investigations 
of  American  geologists  have  proved  that  the  remains  of 
horses  occur  in  the  most  superficial  deposits  of  both  North 
and  South  America,  just  as  they  do  in  Europe.  Therefore, 
for  some  reason  or  other, — no  feasible  suggestion  on  that 
subject,  so  far  as  I  know,  has  been  made, — the  horse  must 
have  died  out  in  this  continent  at  some  period  preceding 
the  discovery  of  America.  Of  late  years  there  has  been 
discovered  in  your  Western  Territories  that  marvellous  ac- 
cumulation of  deposits,  admirably  adapted  for  the  preser- 
vation of  organic  remains,  to  which  I  referred  the  other 
evening,  and  which  furnishes  us  with  a  consecutive  series 
of  records  of  the  fauna  of  the  older  half  of  the  Tertiary 


296    TYPICAL    SYSTEMS    OF    KNOWLEDGE 


epoch,  for  which  we  have  no  parallel  in  Europe.  They 
have  yielded  fossils  in  an  excellent  state  of  conservation 
and  in  unexampled  number  and  variety.  The  researches 


Fore        Hind    Pore 
Foot.       Foot.    Arm. 


Lower 
.    Upper  Molar.    Molar. 


MIOHIPPUS. 

(Anchilherium) 


MESOHIPPUS 


EOCENE. 


OROHIPPUS. 


FIG.  12. 


of  Leidy  and  others  have  shown  that  forms  allied  to  the 
Hipparion  and  the  Anchitherium  are  tP  be  found  among 


HUXLEY    ON    EVOLUTION  297 

these  remains.  And  it  is  only  recently  that  the  admirably 
conceived  and  most  thoroughly  and  patiently  worked-out 
investigations  of  Professor  Marsh  have  given  us  a  just  idea 
of  the  vast  fossil  wealth  and  of  the  scientific  importance 
of  these  deposits.  I  have  had  the  advantage  of  glancing 
over  the  collections  in  Yale  Museum,  and  I  can  truly  say 
that,  so  far  as  my  knowledge  extends,  there  is  no  collection 
from  any  one  region  and  series  of  strata  comparable  for 
extent,  or  for  the  care  with  which  the  remains  have  been 
got  together,  or  for  their  scientific  importance,  to  the  series 
of  fossils  which  he  has  deposited  there.  This  vast  collec- 
tion has  yielded  evidence  bearing  upon  the  pedigree  of  the 
horse  of  the  most,  striking  character.  It  tends  to  show 
that  we  must  look  to  America,  rather  than  to  Europe,  for 
the  original  seat  of  the  equine  series;  and  that  the  archaic 
forms  and  successive  modifications  of  the  horse's  ancestry 
are  far  better  preserved  here  than  in  Europe. 

"  Professor  Marsh's  kindness  has  enabled  me  to  put  be- 
fore you  a  diagram,  every  figure  in  which  is  an  actual  repre- 
sentation of  some  specimen  which  is  to  be  seen  at  Yale 
at  this  present  time  (Fig.  12). 

"  The  succession  of  forms  which  he  has  brought  together 
carries  us  from  the  top  to  the  bottom  of  the  Tertiaries. 
Firstly,  there  is  the  true  horse.  Next  we  have  the  American 
Pliocene  form  of  the  horse  (Pliohippus)  ;  in  the  conforma- 
tion of  its  limbs  it  presents  some  very  slight  deviations 
from  the  ordinary  horse,  and  the  crowns  of  the  grinding 
teeth  are  shorter.  Then  comes  the  Protohippus,  which 
represents  the  European  Hipparion,  having  one  large  digit 
and  two  small  ones  on  each  foot,  and  the  general  charac- 
ter of  the  fore-arm  and  leg  to  which  I  have  referred.  But 
it  is  more  valuable  than  the  European  Hipparion  for  the 
reason  that  it  is  devoid  of  some  of  the  peculiarities  of  that 
form — peculiarities  which  tend  to  show  that  the  European 
Hipparion  is  rather  a  member  of  a  collateral  branch  than1 
a  form  in  the  direct  line  of  succession.  Next,  in  the  back- 
ward order  in  time,  is  the  Miohippus,  which  corresponds 
pretty  nearly  with  the  Anchitherium  of  Europe.  It  pre- 
sents three  complete  toes — one  large  median  and  two  smal- 
ler lateral  ones ;  and  there  is  a  rudiment  of  that  digit  which 
answers  to  the  little  finger  of  the  human  hand. 

"  The   European   record   of  the  pedigree   of  the  horse 


298    TYPICAL    SYSTEMS    OF    KNOWLEDGE 

stops  here;  in  the  American  Tertiaries,  on  the  contrary, 
the  series  of  ancestral  equine  forms  is  continued  into  the 
Eocene  formations.  An  older  Miocene  form,  termed  Meso- 
hippus,  has  three  toes  in  front,  with  a  large  splint-like 
rudiment  representing  the  little  finger,  and  three  toes  be- 
hind. The  radius  and  the  ulna,  the  tibia  and  the  fibula, 
are  distinct,  and  the  short-crowned  molar  teeth  are  Anchi- 
theroid  in  pattern. 

"  But  the  most  important  discovery  of  all  is  the  Oro- 
hippus,  which  comes  from  the  Eocene  formation,  and  is  the 
oldest  member  of  the  equine  series,  as  yet  known.  Here 
we  find  four  complete  toes  on  the  front  limb,  three  toes 
on  the  hind  limb,  a  well-developed  ulna,  a  well-developed 
fibula,  and  short-crowned  grinders  of  simple  pattern. 

"  Thus,  thanks  to  these  important  researches,  it  has  be- 
come evident  that,  so  far  as  our  present  knowledge  ex- 
tends, the  history  of  the  horse-type  is  exactly  that  which 
could  have  been  predicted  from  a  knowledge  of  the  prin- 
ciples of  evolution.  And  the  knowledge  we  now  possess 
justifies  us  completely  in  the  anticipation  that  when  the 
still  lower  Eocene  deposits,  and  those  which  belong  to  the 
Cretaceous  epoch,  have  yielded  up  their  remains  of  ances- 
tral equine  animals,  we  shall  find,  first,  a  form  with  four 
complete  toes  and  a  rudiment  of  the  innermost  first  digit 
in  front,  with  probably,  a  rudiment  of  the  fifth  digit  in 
the  hind  foot ; 13  while,  in  still  older  forms,  the  series  of 
digits  will  be  more  and  more  complete,  until  we  come  to  the 
five-toed  animals,  in  which,  if  the  doctrine  of  evolution  is 
well-founded,  the  whole  series  must  have  taken*  its  origin. 

"  This  is  what  I  mean  by  the  demonstrative  evidence 
of  evolution.  An  inductive  hypothesis  is  said  to  be  demon- 
strated when  the  facts  are  shown  to  be  in  entire  accordance 
with  it.  If  that  is  not  scientific  proof,  there  are  no  merely 
inductive  conclusions  which  can  be  said  to  be  proved.  And 
the  doctrine  of  evolution,  at  the  present  time,  rests  upon 
exactly  as  secure  a  foundation  as  the  Copernican  theory 
of  the  motions  of  the  heavenly  bodies  did  at  the  time  of  its 
promulgation.  Its  logical  basis  is  precisely  of  the  same 
character — the  coincidence  of  the  observed  facts  with  theo- 
retical requirements. 

is  Remains   of  animals  corresponding  very  closely  to  this   de- 
scription were  afterwards  discovered. 


HUXLEY    ON    EVOLUTION  299> 

"  Tl:e  only  way  of  escape,  if  it  be  a  way  of  escape,  from* 
the  conclusions  which  I  have  just  indicated,  is  the  suppo- 
sition that  all  these  different  equine  forms  have  been 
created  separately  at  separate  epochs  of  time;  and,  I  re- 
peat, that  of  such  an  hypothesis  as  this  there  neither  is, 
nor  can  be,  any  scientific  evidence;  and  assuredly,  so  far 
as  I  know,  there  is  none  which  is  supported,  or  pretends 
to  be  supported,  by  evidence  or  authority  of  any  other 
kind.  I  can  but  think  that  the  time  will  come  when  such 
suggestions  as  these,  such  obvious  attempts  to  escape  the 
force  of  demonstration,  will  be  put  upon  the  same  footing 
as  the  supposition  made  by  some  writers,  who  are,  I  be- 
lieve, not  completely  extinct  at  present,  that  fossils  are 
mere  simulacra,  are  no  indications  of  the  former  existence 
of  the  animals  to  which  they  seem  to  belong ;  but  that  they 
are  either  sports  of  Nature,  or  special  creations.  .  .  . 

"  In  fact,  the  whole  evidence  is  in  favor  of  evolution,  and 
there  is  none  against  it.  And  I  say  this,  although  perfectly 
well  aware  of  the  seeming  difficulties  which  have  been 
built  up  upon  what  appears  to  the  uninformed  to  be  a 
solid  foundation.  I  meet  constantly  with  the  argument 
that  the  doctrine  of  evolution  cannot  be  well  founded,  be- 
cause it  requires  the  lapse  of  a  very  vast  period  of  time; 
while  the  duration  of  life  upon  the  earth,  thus  implied,  is 
inconsistent  with  the  conclusions  arrived  at  by  the  as- 
tronomer and  the  physicist.  I  may  venture  to  say  that  I 
am  familiar  with  those  conclusions,  inasmuch  as  some  years 
ago,  when  President  of  the  Geological  Society  of  London, 
I  took  the  liberty  of  criticising  them,  and  of  showing  in 
what  respects,  as  it  appeared  to  me,  they  lacked  complete 
and  thorough  demonstration.  But,  putting  that  point  aside, 
suppose  that,  as  the  astronomers,  or  some  of  them,  and 
some  physical  philosophers,  tell  us,  it  is  impossible  that  life 
could  have  endured  upon  the  earth  for  as  long  a  period 
as  is  required  by  the  doctrine  of  evolution — supposing  that 
to  be  proved — I  desire  to  be  informed  what  is  the  founda- 
tion for  the  statement  that  evolution  does  require  so  great 
a  time.  The  biologist  knows  nothing  whatever  of  the 
amount  of  time  which  may  be  required  for  the  process  of 
evolution.  It  is  a  matter  of  fact  that  the  equine  forms, 
which  I  have  described  to  you,  occur  in  the  order  stated  in 
the  Tertiary  formations,  But  I  have  not  the  slightest 


300    TYPICAL    SYSTEMS    OF    KNOWLEDGE 

means  of  guessing  whether  it  took  a  million  of  years,  or 
ten  millions,  or  a  hundred  millions,  or  a  thousand  millions 
of  years,  to  give  rise  to  that  series  of  change. 

"  A  biologist  has  no  means  of  arriving  at  any  conclusion 
as  to  the  amount  of  time  which  may  be  needed  for  a  certain 
quantity  of  organic  change.  He  takes  his  time  from  the 
geologist.  The  geologist,  considering  the  rate  at  which  de- 
posits are  formed  and  the  rate  at  which  denudation  goes 
on  upon  the  surface  of  the  earth,  arrives  at  more  or  less 
justifiable  conclusions  as  to  the  time  required  for  the  de- 
posit of  a  certain  thickness  of  rocks ;  and  if  he  tells  me 
that  the  Tertiary  formations  required  500,000,000  years 
for  their  deposit,  I  suppose  he  has  good  ground  for  what 
he  says,  and  I  take  that  as  a  measure  of  the  duration  of 
the  evolution  of  the  horse  from  the  Orohippus  up  to  its 
present  condition.  And,  if  he  is  right,  undoubtedly  evolu- 
tion is  a  very  slow  process,  and  requires  a  great  deal  of 
time.  But  suppose,  now,  that  an  astronomer  or  a  physicist 
— for  instance,  my  friend,  Sir  William  Thomson — tells  me 
that  my  geological  authority  is  quite  wrong;  and  that  he 
has  weighty  evidence  to  show  that  life  could  not  possibly 
have  existed  upon  the  surface  of  the  earth  500,000,000 
years  ago,  because  the  earth  would  have  then  been  too  hot 
to  allow  of  life,  my  reply  is :  '  That  is  not  my  affair ;  set- 
tle that  with  the  geologist,  and  when  you  have  come  to  an 
agreement  among  yourselves,  I  will  adopt  your  conclu- 
sion/ We  take  our  time  from  the  geologists  and  physicists ; 
and  it  is  monstrous  that,  having  taken  our  time  from  the 
physical  philosopher's  clock,  the  physical  philosopher  should 
turn  round  upon  us,  and  say  we  are  too  fast  or  too  slow. 
What  we  desire  to  know  is,  is  it  a  fact  that  evolution*  took 
place  ?  As  to  the  amount  of  time  which  evolution  may  have 
occupied,  we  are  in  the  hands  of  the  physicists  and  as- 
tronomers, whose  business  it  is  to  deal  with  those  questions." 


INDEX 


Abstractions,    45 

Abstract  terms,  54 

Aikins,   163,  205 

Amphibology,  73 

Analogy,   251;   rules   of,  252 

Analysis,    46,    88 

Antecedent   probability,   277 

Astronomy,  265 

Average  deviation,  206 

A ve_ragev.  deviation   from,   205 

Average  error,  206 

Averages,  195,  198;  arithmet- 
ical, 198;  geometrical,  204; 
the  median,  202;  the  mode, 
201 ;  "  weighted  "  averages, 
199 

Bain,  104,  271 

Baldwin,  11,  238 

Biology,  35,  42,  208,  262 

Bosanuqet,  34 

Bowley,  192,  194,  200,  202,  203, 

204,  207,  229,  230. 
Burnet,  249 

Causal  law,  81,  82 
Cause,  81 
Chamberlain,  250 
Chemistry,  262 
Circumstantial  evidence,  279 
Collective  judgments,  86 
Collective  terms,  56 
.Collusion,   276 
Composition  of  causes,  97,  193 


Classification,  6,  32,  49,  79,  195; 
artificial,  33;  diagnostic,  33; 
index,  32;  natural,  33;  req- 
uisites of,  40,  49 

Common  sense,  1 

Comparison  of   quantities,  210 

Composition,    fallacy   of,  57 

Concept,  conception,  45 

Concrete  terms,  54 

Contradictory  propositions,  114 

Contraposition,  122 

Contrary  propositions,  114 

Conversion,  119 

Correlation,  191 

Counteracting  causes,  97,  193 

Cramer,  248,  250 

Cross-division,  41 

Curves,  226 

Cuvier,  12 

Darwin,  248,  249 

Deduction,     110;     a     part     of 

scientific  method,  2 
Definition,  57;  defects  of,  60 
DeMorgan,  77 
Deviations     from    an    average, 

205 

Dilemma,  The,  159 
Discrimination,  45 
Disjunctive  reasoning,  157 
Distributive  terms,  56 
Distribution  of  terms,  71 
Division,   37;   dichotomous,  38; 

incomplete,  40;  rules  of,  40; 

fallacy  of,  56 


801 


302 


INDEX 


Documents,  266 

Elimination  in  the  inductive 
methods,  96 

Enthymeme,    151 

Enumeration,  complete,  84;  in- 
complete or  simple,  83,  190 

Error,  206;   curve  of,  231 

Errors,  three  kinds,  18;  causes 
of,  19 

Euclid,  258 

Euler's  Method,  72,  120 

Evidence,  48 ;  circumstantial, 
279;  external,  270;  hearsay, 
278;  indirect,  278;  internal, 
270 

Exceptive  propositions,  76 

Exclusive   propositions,   75 

Experiment,  24 

Explanation,  237;  general,  240; 
specific,  240,  244 

External  evidence,  270 

Extra-syllogistic  reasoning,  162 

Fallacies,  formal,  138,  173;  of 
accent,  76;  of  amphibology, 
73;  of  assumption,  171;  of 
converse  accident,  55;  of 
composition,  57;  of  division, 
57;  of  figure  of  speech,  76; 
of  four  terms,  138;  of  hypo- 
thetical reasoning,  157;  of 
illicit  major,  141;  of  illicit 
minor,  141 ;  of  missing  the 
point,  171 ;  of  non-sequitur, 
174;  of  perception,  16;  of 
petitio  principii,  172;  of  post 
hoc  ergo  propter  hoc,  174;  of 
undistributed  middle,  138 

Figures  of  the  syllogism,  126, 
142;  principles  of,  126;  rules 
for,  126 


Fison,  284 

Fowler,  90 

Fundamentun  division™,  34,  41 

Facts,  13 

Galton,  203 
Generalization,  79 
General  terms,  52 
Genus,  41 
Geology,   264 
Geometry,  258 
Gomperz,  255 
Graphic  method,  266 

Hadley,  249 

Hayward,  276 

Hearsay  evidence,  278 

Helmholz,  208 

Hibben,  111,  123 

History,  264 

Hobhouse,  240,  253 

Huxley,  1,  12,  36,  248,  278 

Hypotheses,  246;  value  of, 
246;  value  of  erroneous,  249; 
how  suggested,  251;  requi- 
sites of,  253 

Hypothetical  reasoning,  157; 
rules  of,  157 

Hyslop,  38,  73,  75,  120 

Induction,  2,  79;  perfect,  85; 
mathematical,  168 

Inductive  inference,  SI 

Indjiclise-jaethods^  £8 ;  agree- 
ment, 90;  difference,  95;  the 
joint  method,  98;  concomi- 
tant variations,  102;  residues, 
104 

Inference,  6,  14,  15,  29 

Infima  species,  42 

Internal  evidence,  270 


INDEX 


303 


James,   21,   113,   208,   263,   280; 

theory  of  the  emotions,  280 
Jevons,  33,  36,  76,  150,  209,  219, 

221,  239 
Joseph,  69 

Kant,  4,  9 

Knowledge,    the    beginning    of, 

3;  the  sources  of,  5;  organ- 

izing, 6 

Langlois    and    Seignobos,    250, 

266,  269,  279 
Language,  7,  48 

X»aw,  79,  237;  how  discovered. 
^~8,  189  ~ 

Laws  of  thought,  1,  10 
Linnaeus,  34 
Locke,  4,  9,  76 
Lotze,  223 

Material  facts,  266 
Mayo-Smith,  196 
Meaning,  47 
Measurement,   208 
Mechanics,   262 


Median  error,  206      , 
MemoryTsT  26,  48  ^ 
Mendel's  Law,  263 
Methods,  inductive,  88 
Mill,  84,  86,  91,  95,  96,  101,  102, 

105 

Minto,  251,  255 
Mode,  the,  201 

Moods    of   the    syllogism,    140 
Muirhead,  245 

Natural  classifications,  33 
Natural  science,  4,  12 
Negative  evidence,  276 
Newton,  247 


Observation,     18,     48,     79,    88; 

mistakes  of,  18 
Obversion,  121 

Opposition  of  propositions,  114 
Order,  42 

Pearson,  32,  192,  208 

Perception,  53  13 ;  "  fallacies  " 
of,  16;  how  tested,  23 

Predicables,  60 

Predicate,  68 

Plurality  of  causes,  94,   193 

Porphyry,  37 

Premises,   126 

Presuppositions  of  knowledge, 
9 

Proof,  166;  direct,  166;  indi- 
rect, 166;  in  geometry,  168 

Probability,  213 ;  curve  of,  231 ; 
deduction  of,  216;  dangers  in 
interpreting,  223 

Probable  error,  206 

Propositions,  66;  (juantity  and 
quality  of,  66;  and  terms, 
68;  ambiguous,  73;  exceptive, 
76;  exclusive  75 

Pro-syllogism  and  epi-syllo- 
gism,  152 

Psychology,  262 

Punnett,  253 

Reduction    of   the    moods    and 

figures,  158 
Romanes,  247 
Russell,  59 

Scientific  law,  8 

Science  and  common  sense,  1 

Science,  259 

Scott,  264 

Sedjjwick  and  Wilson,  35 


304 


INDEX 


Seignobos,  Langlois  and,  250, 
266,  269,  279 

Self-evident  propositions,  79 

Sigwart,  196,  243,  251 

Singular  terms,  52 

Sorites,  155 

Species,  41 

Spencer,   61 
_Statistics,    189 ;    collection    of, 

^1931 T31";  tabulation,  194; 
summary,  194;  critical  exam- 
ination of,  194;  often  un- 
necessary, 195;  often  inappli- 
cable, 196 

Subalterns,  114 

Subcontraries,  114 

Subject,  68;  grammatical,  68; 
logical,  68;  metaphysical  or 
ultimate,  69 

Sui  generis,  42 

Summun  genus,  41 

Syllogism,  111;  criticism  of, 
111;  principles  of,  126;  rules 
of,  137 

Symbols,  47 


Systematic  knowledge,  111 

Terms,  49;  distribution  of,  71; 
generalization  of,  50;  spe- 
cialization of,  50;  transfer  of 
meaning  of,  51;  kinds  of,  52; 
and  propositions,  68 

Testimony,  6,  28,  266;  sources 
of  error  in,  28 

Testing  inductive  inference,  83, 
89 

Testing  perceptions,  23 

Thorndike,   192,  211,  234,  263 

Tradition,  278 

Variety,  42 
Veblen,  258 

Verification,  8,  81,  86,  110 
Voltaire,  274 

Washburn,  253 
Witness,  The,  269 
Wilson,  Sedgwick  and,  35 

Yerkes,  263 
Young,  197 


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